When two governments sit down to negotiate a trade deal, an arms treaty or a climate pledge, it is tempting to picture the talks as a contest between two players. Each state has its interests, each side bargains, and the outcome reflects who is stronger or more skillful. Anyone who has watched a real negotiation knows this picture leaves out half the story. The diplomats at the table are also answering to legislatures, parties, ministries, unions, business lobbies and voters back home. A deal that looks sensible at the summit can die in a parliament weeks later.
Two-level game theory is the best-known attempt to model that double bind. It was introduced by the American political scientist Robert D. Putnam in 1988, and it has since become one of the standard frameworks for studying how domestic and international politics interact. This article explains where the idea came from, how it works, what its key concepts mean, how later scholars extended and criticized it, and why it remains useful for understanding the news.
The basic idea in one paragraph
Putnam's model treats an international negotiation as two games played at the same time. At Level I, the international level, a chief negotiator (often a head of government or a senior minister) bargains with foreign counterparts toward a tentative agreement. At Level II, the domestic level, groups inside each country decide whether to accept, or "ratify," that agreement. The negotiator sits at both tables at once. A move that is rational at one table can be foolish at the other, and a skilled player can sometimes use a move at one table to change the balance of forces at the other. In Putnam's own phrasing in the article, the political complexities for players in this two-level game are staggering.
Origins: Putnam's 1988 article
The theory comes from a single, heavily cited journal article: Robert D. Putnam, "Diplomacy and Domestic Politics: The Logic of Two-Level Games," published in International Organization, volume 42, number 3 (Summer 1988), pages 427–460. According to the article's own acknowledgments, an earlier version was presented in 1986 at the annual meeting of the American Political Science Association. Putnam, then at Harvard, is better known to the general public for his later work on social capital, including the book Bowling Alone, but in international relations the two-level games article is his signature contribution.
The article was not written in a vacuum. Putnam surveyed earlier attempts to connect domestic and international politics and found them wanting. He noted that much of the existing literature consisted either of long lists of "domestic influences" on foreign policy or general remarks that domestic and international affairs were somehow "linked." He discussed James Rosenau's work on "linkage politics," the regional-integration studies of Karl Deutsch and Ernst Haas, the "bureaucratic politics" school associated with Graham Allison, and the "state-centric" work of Peter Katzenstein and Stephen Krasner, which emphasized "state strength." His complaint about the state-centric approach was that it treated "the state" as a single actor, when in practice central decision-makers routinely disagree with each other about what the national interest requires. He suggested that if "the state" means central decision-makers, it should be treated as a plural noun.
Putnam also drew on the labor-negotiation literature, especially Richard Walton and Robert McKersie's 1965 "behavioral theory" of labor negotiations, which had already shown that the assumption of a unitary actor on each side is often misleading. He quoted Robert Strauss, the U.S. Special Trade Representative during the Tokyo Round of trade talks, who said he had spent as much time negotiating with domestic constituents and members of Congress as with foreign trading partners.
Putnam was modest about what he was offering. He called the two-level game a metaphor, not yet a formal theory, and quoted the philosopher Max Black's remark that perhaps every science must start with metaphor and end with algebra. He acknowledged that working out formal solutions to two-level games would be a difficult challenge.
The case that inspired the theory: the 1978 Bonn summit
Putnam had studied the annual economic summits of the major Western powers, the group now known as the G7, in the late 1970s, partly with C. Randall Henning and Nicholas Bayne. The case that anchors the 1988 article is the Bonn summit of July 1978.
The background was a stalled world economy. In the run-up to the summit, the United States and others pressed West Germany and Japan to stimulate their economies and act as "locomotives" for global growth. The Germans and Japanese resisted, arguing that prudent economic managers should not be asked to bail out spendthrifts. At the same time, President Jimmy Carter's energy program was stuck in Congress, and German Chancellor Helmut Schmidt led complaints about America's appetite for imported oil and its apparent lack of concern about the falling dollar.
At Bonn, a broad package was agreed. According to Putnam's account:
- Helmut Schmidt agreed to additional fiscal stimulus amounting to about 1 percent of gross national product.
- Jimmy Carter committed to decontrolling domestic U.S. oil prices by the end of 1980.
- Japanese Prime Minister Takeo Fukuda pledged new efforts to reach a 7 percent growth rate.
- Secondary elements included French and British agreement to move forward in the Tokyo Round trade negotiations, Japanese measures to boost imports and restrain exports, and a general U.S. promise to fight inflation.
Putnam observed that virtually all parts of the package were actually implemented. Carter, for example, decided in April 1979 on gradual administrative decontrol that would bring U.S. oil prices up to world levels by about October 1981.
What interested Putnam was not whether the package was wise economics, but how it became politically possible. His research suggested two things. First, the key governments adopted policies different from those they would have pursued without the international negotiation. Second, the deal was possible only because, inside each government, a powerful minority already favored the policy being demanded from abroad.
In Germany, he argued, contrary to public mythology, the Bonn agreement was not imposed on a reluctant country. Officials in the Chancellor's office and the Economics Ministry, along with the Social Democratic Party and the trade unions, had privately concluded in early 1978 that more stimulus was desirable, especially with elections approaching in 1980. They faced opposition from the Finance Ministry, the Free Democratic Party (a coalition partner), the business and financial communities, and the leadership of the Bundesbank. Schmidt publicly appeared reluctant, but in Putnam's account he let himself be pushed into a policy he privately supported and that would have been costly or perhaps impossible to pass at home without the summit agreement.
Japan showed a similar pattern. A coalition of business interests, the Ministry of International Trade and Industry, the Economic Planning Agency and some expansion-minded politicians in the Liberal Democratic Party used American pressure as an argument against the resistance of the Ministry of Finance. Putnam reports that one disappointed Finance Ministry official put the outcome at roughly 70 percent external pressure and 30 percent internal politics, while a MITI official called it about fifty-fifty.
In the United States, the economic officials who favored a tougher energy policy faced resistance from the President's political advisers and from opponents in Congress. American negotiators had in fact invited their foreign counterparts to put more pressure on the United States over oil imports.
Putnam's conclusion was that neither a purely domestic analysis nor a purely international one could explain the episode. Explanations running only from domestic causes to international effects, or only from international causes to domestic effects, would be "partial equilibrium" analyses. What was needed was something closer to "general equilibrium": a framework that captured how the domestic politics of several countries became entangled through an international negotiation.
How the game works: Level I and Level II
To make the idea manageable, Putnam set out a stylized scenario. Negotiators representing two organizations meet to reach an agreement, subject to the constraint that any tentative agreement must be ratified by their respective organizations. The negotiators might be heads of government, labor and management representatives, coalition party leaders, a finance minister negotiating with an International Monetary Fund team, or leaders of a U.S. House–Senate conference committee.
He then divided the process analytically into two stages:
- Level I: bargaining between the negotiators, leading to a tentative agreement.
- Level II: separate discussions within each group of constituents about whether to ratify the agreement.
Putnam stressed that this sequence is a simplification. In real negotiations, expectations about Level II shape Level I from the start. Negotiators consult domestic groups before they open talks, and the anticipated rejection of a deal at home can abort it before any formal vote. He gave the example of the reported arms-for-hostages arrangement between the United States and Iran in the mid-1980s, which collapsed once it became public and therefore subject to de facto "ratification."
What "ratification" means
Putnam used "ratification" in a deliberately broad sense. It can mean a formal vote, such as the two-thirds majority the U.S. Senate needs to approve a treaty, but it can be any decision process at Level II that is needed to endorse or implement a Level I agreement. Level II actors can be bureaucratic agencies, interest groups, social classes or "public opinion." If labor unions in a debtor country refuse to cooperate with an austerity program their government has agreed with the IMF, Putnam wrote, Level II ratification can be said to have failed.
Ratification does not need to be democratic. Putnam noted that in 1930 Japan's Meiji Constitution was interpreted to give the military a special role in ratifying the London Naval Treaty. The one formal rule he insisted on is that, because the same agreement must be accepted on both sides, a Level I agreement cannot be amended at Level II without reopening the international talks. Ratification is essentially a yes-or-no vote.
The central concept: the win-set
The most important idea in two-level game theory is the win-set. Putnam defined the win-set of a given Level II constituency as the set of all possible Level I agreements that would "win," meaning gain the necessary majority among the constituents, when simply voted up or down. Putnam credited the concept of win-sets to the work of Kenneth Shepsle and Barry Weingast.
Win-sets matter for two separate reasons.
First, larger win-sets make agreement more likely. Any successful agreement must fall inside the win-set of every party. Agreement is therefore possible only if the win-sets overlap, and the larger each win-set, the more likely they are to overlap. The smaller the win-sets, the greater the risk that negotiations break down. Putnam's example was the long negotiations before the 1982 conflict between Britain and Argentina over the Falkland Islands. Several provisional agreements were rejected in one capital or the other for domestic political reasons, and when it became clear that the British and Argentine win-sets did not overlap at all, war became, in his words, virtually inevitable.
Second, the relative size of win-sets affects who gets the better deal. The larger a negotiator's win-set is perceived to be, the more he or she can be pressured by the other side. Conversely, a small domestic win-set can be a bargaining advantage. The negotiator can say, in effect, "I'd like to accept your proposal, but I could never get it accepted at home."
The Schelling insight: weakness as strength
Putnam pointed out that this second principle had been noticed almost thirty years earlier by the economist Thomas Schelling in The Strategy of Conflict (1960). Schelling observed that a negotiator's power often rests on a manifest inability to make concessions. When an executive negotiates under authority delegated by a legislature and its position is fixed by law, its firm position is visible to the other side. Schelling also warned that such tactics run the risk of creating a fixed position beyond what the other side can concede, raising the chance of stalemate.
Later scholars came to call the idea that domestic constraints can strengthen a negotiator's hand the "Schelling conjecture." Putnam's own examples include U.S. negotiators using the difficulty of Senate ratification as leverage. During the Panama Canal treaty negotiations of the 1970s, according to sources Putnam cites, the U.S. Secretary of State repeatedly warned the Panamanians that a new treaty had to be acceptable to at least 67 senators, and Carter wrote to Panama's leader, Omar Torrijos, that additional U.S. concessions would seriously threaten Senate ratification.
Putnam also floated a provocative implication: a developing-country leader with a relatively weak domestic position might be able to bargain harder with international creditors than a leader with a strong domestic position, other things being equal. He illustrated the idea with a hedged pairing of Raúl Alfonsín's Argentina and Miguel de la Madrid's Mexico, phrased as questions rather than firm claims.
Voluntary and involuntary defection
The possibility that ratification might fail led Putnam to distinguish two kinds of broken promise. Voluntary defection is the familiar problem in game theory, such as the prisoner's dilemma, where a rational egoist reneges on a deal in the absence of enforceable contracts. Involuntary defection is different: the negotiator wants to keep the promise but cannot, because domestic ratification fails.
Putnam gave several examples. Congress failed to ratify the abolition of the "American Selling Price" system of customs valuation that U.S. negotiators had agreed to in the Kennedy Round of trade talks in the 1960s. Japanese Prime Minister Eisaku Sato was unable to deliver on a promise made to President Richard Nixon during the U.S.–Japan textile dispute. And, Putnam wrote, a major obstacle to Western economic coordination in 1985–1987 was German fear that the Reagan administration would be politically unable to deliver on any commitment to cut the U.S. budget deficit.
The smaller the win-sets, the greater the risk of involuntary defection. Putnam noted that at his press conference after the Bonn summit, Carter emphasized that each leader had been careful not to promise more than he could deliver. Fear of involuntary defection can be as damaging to cooperation as fear of cheating, and the two can be hard to tell apart, especially when a strategic negotiator tries to present a voluntary defection as an involuntary one.
What determines the size of a win-set?
Putnam identified three broad sets of factors.
1. Level II preferences and coalitions
Any testable two-level theory, Putnam argued, must be rooted in a theory of domestic politics: who has power and what they want. A simple principle is that the lower the cost of "no agreement" to domestic constituents, the smaller the win-set. Ratification pits the proposed agreement not against all possible alternatives but only against no agreement. Groups for whom no agreement is cheap will be more skeptical of deals.
Putnam suggested that the balance between "isolationist" forces, which resist international cooperation in general, and "internationalist" forces, which offer something close to blanket support, shapes win-set size. He expected blanket support for international agreements to be greater in smaller, more dependent and more open economies than in more self-sufficient countries like the United States, because the cost of no agreement is higher for their citizens. More self-sufficient states with smaller win-sets should, other things equal, make fewer international agreements and drive harder bargains.
He also distinguished between homogeneous and heterogeneous domestic conflicts, borrowing Walton and McKersie's terms "boundary" and "factional" conflict. In a homogeneous case, almost everyone at home wants more from the other side, and the main disagreement is between "hawks" and "doves" over how hard to push. Putnam suggested arms control talks such as SALT, the Panama Canal negotiations and the Arab-Israeli conflict as possible examples. In such cases, the more the negotiator wins abroad, the better the chances at home, and domestic hardliners can be used as a bargaining threat.
In a heterogeneous case, an agreement cuts across domestic groups unequally. An internationally coordinated reflation program might be opposed both by bankers who think it goes too far and by unions who think it does not go far enough. Putnam noted that in 1919 some Americans opposed the Treaty of Versailles as too harsh on the defeated powers and others as too lenient. Here "more is better" does not apply, and something surprising becomes possible: the negotiator may find silent allies at the other side's domestic table. German unions might welcome foreign pressure for fiscal expansion; Italian bankers might welcome foreign pressure for monetary austerity. This, Putnam said, was his interpretation of the Bonn deal. A government that is internally divided can sometimes be more likely to reach an international agreement than one firmly committed to a single policy.
Putnam also discussed issue linkage. When a negotiation covers several issues, different domestic groups care about different parts of the package, and the negotiator must make cross-issue trade-offs. He described a special kind of linkage, which he called synergistic linkage, in which an international deal creates a policy option that did not exist domestically. For example, if most domestic groups oppose oil price decontrol but some would switch their votes in exchange for more jobs in export industries, a deal that brings faster growth abroad can change the domestic outcome. Putnam called this a crucial element in the Bonn accord and expected synergistic linkage to become more common as economic interdependence grows.
2. Level II institutions
Ratification procedures clearly affect win-set size. If a two-thirds vote is required, the win-set will almost certainly be smaller than under a simple majority. Putnam quoted Carter's own memoir lamenting that under the U.S. Constitution, 34 of 100 senators can block any treaty. The U.S. separation of powers, Putnam argued, imposes a tighter constraint on the American win-set than exists in many other countries. That strengthens U.S. negotiators' bargaining hand but reduces the scope for cooperation and makes partners wary.
He described how the U.S. Trade Act of 1974 tried to address this by guaranteeing a single up-or-down congressional vote on trade agreements, combined with a system of private-sector advisory committees to keep domestic groups informed. Informal practices matter too: Putnam suggested that the Japanese political habit of seeking broad domestic consensus before acting constrains the Japanese win-set, while strong party discipline in a governing party expands a win-set.
Putnam also tied this to the debate on "state strength." Greater autonomy of central decision-makers from domestic pressure enlarges the win-set and makes agreement more likely. An independent central bank, for example, increases the chances of international monetary cooperation. But the same logic implies that a state strongly insulated from domestic pressure has a weaker bargaining position, because its diplomats cannot credibly claim that domestic forces prevent them from accepting a bad deal. He cited Schelling's observation that representatives of an entrenched dictatorship are less able than democratic negotiators to make that argument.
He added that many real negotiations involve more than two levels. Changes to the European Community's Common Agricultural Policy under the Treaty of Rome required unanimous approval in the Council of Ministers, after which each government needed domestic approval, sometimes including approval inside coalition parties.
3. Level I negotiators' strategies
Each negotiator has an unambiguous interest in enlarging the other side's win-set, but mixed motives about their own. A bigger own win-set makes agreement easier but weakens one's bargaining position. Mobilizing domestic support for a hard line, for instance by talking about "unfair trade practices" abroad, can signal commitment, but it can also harden domestic attitudes and make later ratification harder.
To expand a win-set, a negotiator can use side-payments and generic goodwill. Putnam pointed out that the Carter administration offered public-works projects and similar favors to win over hesitant senators on the Panama Canal treaties. The two-level view stresses that a side-payment should be judged by its marginal effect on the probability of ratification, not by its total value to the nation. A concession that pleases a committed free-trader or a confirmed protectionist does little; one that moves an undecided vote does a lot. A negotiator with high domestic popularity also finds ratification easier, which is why each negotiator has an interest in the popularity of the other, and why foreigners prefer to deal with a head of government rather than a lower official.
Uncertainty, bluffing and "kinky" win-sets
Real negotiators are often poorly informed about the domestic politics on the other side. Putnam reported that at Bonn in 1978 most American officials did not appreciate the complicated game Schmidt was playing at home.
Uncertainty cuts both ways. In purely distributive bargaining, negotiators have an incentive to understate their win-sets, claiming they cannot get a better deal past their domestic audience. But uncertainty about the other side's win-set also raises fears of involuntary defection, and a party unsure the other can deliver will demand more compensation. Putnam suggested that a negotiator therefore wants to convince the other side that the win-set is "kinky," meaning that the proposed deal will certainly be ratified but a deal slightly more favorable to the opponent will not. He gave the example of Carter sending Senator Robert Byrd to Bonn before the 1978 summit to persuade Schmidt that immediate oil price decontrol was politically impossible but that decontrol by 1981 was feasible.
Restructuring and reverberation
Putnam noted that much of what happens in bargaining involves trying to reshape the game itself, including the other side's perception of the costs of no agreement. Governments do try to expand each other's win-sets through diplomacy aimed at foreign domestic audiences: lobbying opinion leaders, cultivating opposition parties, or, in his examples, Japanese officials visiting the U.S. Congress and British diplomats courting Irish-American leaders.
He gave the example of 1977 negotiations between the IMF and Italy, in which the IMF consulted directly with union and left-wing leaders and restructured its proposal around long-term investment and recovery to reduce the risk of involuntary defection.
Reverberation is the term Putnam used for international pressure that changes the domestic balance of opinion. He cited Dieter Hiss, the German "sherpa" for the 1978 summit, who wrote that summits change national policy only insofar as they mobilize or change public opinion and the attitude of political groups, and that it is often enough to tip a strong blocking minority into a narrow majority. Reverberation can also be negative, when foreign pressure provokes a backlash, particularly if the source is seen as an adversary. Putnam argued that reverberation and synergistic linkage prevent analysts from taking a tempting shortcut: if domestic preferences were fixed, domestic politics could be modeled separately and fed into the international game. Because international bargaining can change those preferences, the two levels cannot be modeled independently.
The chief negotiator's own interests
So far the negotiator has been treated as an honest broker. Putnam relaxed that assumption. Drawing on principal-agent theory, he noted that the chief negotiator's preferences may differ from those of constituents. He listed motives including strengthening his or her own domestic position, shifting the domestic balance toward policies he or she already prefers, and pursuing a personal conception of the national interest. He pointed to IMF stabilization programs, sometimes misleadingly described as "imposed" by the Fund, in which domestic conservatives in Italy in 1974 and 1978 used IMF pressure to make changes that would otherwise have been impossible.
His most striking example concerned the Treaty of Versailles. Putnam wrote that there was strong evidence that perhaps 80 percent of the American public and Senate in 1919 favored ratification with certain reservations, provided the other key signatories accepted them. It was Woodrow Wilson himself, Putnam argued, who vetoed this ratifiable deal, reportedly telling the French ambassador that he would consent to nothing.
Later developments and criticism
Putnam's article set off a large research program. In 1993, Peter B. Evans, Harold K. Jacobson and Robert D. Putnam edited Double-Edged Diplomacy: International Bargaining and Domestic Politics (University of California Press), a collection of eleven case studies testing and extending the framework, with a concluding chapter by Evans on building an integrative approach.
Several scholars refined or challenged particular parts of the model:
- Leonard J. Schoppa (International Organization, 1993) studied the U.S.–Japan Structural Impediments Initiative, a case of heavy American pressure (gaiatsu) on Japan. He argued that Putnam identified only some of the strategies negotiators use to reshape a counterpart's domestic politics. Besides reverberation and synergistic linkage, he described "participation expansion," bringing new actors and public opinion into decisions previously controlled by small groups, and "alternative specification," influencing which policy options are considered. He concluded that foreign pressure works best under particular domestic conditions.
- Jeffrey W. Knopf (International Organization, 1993), studying the U.S.–Soviet Intermediate-Range Nuclear Forces negotiations, argued that the two-level approach did not clearly distinguish different types of domestic-international interaction and overlooked dynamics involving third parties such as military allies. He proposed a "three-and-three" approach with three forms of interaction and a third level of analysis.
- Jongryn Mo (American Political Science Review, 1995) used formal modeling to ask whether a negotiator would deliberately tie his own hands by giving a domestic agent veto power. He found the answer depends on what the foreign side knows and how far the agent's preferences diverge from the negotiator's, and that, under incomplete information, a surprisingly wide range of agents would be granted a veto because it lets the negotiator send more credible signals.
- Formal work by Keisuke Iida and later Ahmer Tarar, among others, examined when the Schelling conjecture actually holds. A 1996 article by Iida in Public Choice on involuntary defection argued that incomplete information about domestic actors' preferences is crucial for understanding ratification failures. Tarar's work on two-sided domestic constraints suggested that when both sides face constraints under incomplete information, outcomes can run opposite to Schelling's prediction.
The common thread in the critiques is not that Putnam was wrong, but that the metaphor needed sharper definitions, more actors and more attention to information before it could produce precise predictions. Putnam himself had anticipated much of this when he described the article as a starting point.
Two-level games in recent events
The framework continues to be applied to current affairs. The Wikipedia article on the topic gives two illustrations.
Climate change and the Paris Agreement. Climate mitigation creates a free-rider problem, since most states benefit from the efforts of a few large emitters, and negotiations have been shaped by differing views of fairness. The Wikipedia article cites the U.S. withdrawal from the Paris Agreement under the first Trump administration, supported by many Republicans and aligned interest groups, as an example of domestic forces shaping a win-set. In two-level terms, the American domestic table changed, and the set of climate commitments the United States would ratify shrank. Robert Keohane and Michael Oppenheimer's 2016 article on Paris's "pledge and review" design and a 2017 article by Hai-Bin Zhang and colleagues on the reasons for and effects of U.S. withdrawal are cited there as background.
The Falklands. As Putnam himself described, the failure of tentative Anglo-Argentine agreements to win domestic approval left two non-overlapping win-sets.
The same logic helps explain everyday diplomatic behavior: leaders who warn foreign counterparts that "my parliament will never accept this," governments that seek fast-track or single-vote ratification procedures for trade deals, and foreign officials who lobby another country's legislators or public directly.
Strengths and limitations
Strengths. The model replaces the fiction of the unitary state with a realistic picture of negotiators answering to two audiences. It offers a vocabulary — win-sets, involuntary defection, synergistic linkage, reverberation — that applies across trade, finance, security and environmental negotiations. It also explains several counterintuitive facts: that domestic weakness can be a bargaining asset, that a divided government can sometimes make a deal more easily than a united one, and that negotiators often help each other sell the agreement at home.
Limitations. Putnam called it a metaphor, and in its original form it does not produce precise predictions. Measuring a win-set in practice is hard, because it depends on hidden preferences and on expectations that change during the negotiation. As Knopf noted, the two-level frame can be too simple for negotiations with allies or third parties, and multi-level settings like the European Union require more levels. Formal models have shown that the "tied hands" advantage holds only under specific conditions.
Frequently asked questions
Who created two-level game theory? Robert D. Putnam, in the article "Diplomacy and Domestic Politics: The Logic of Two-Level Games," International Organization 42(3), 1988, pages 427–460.
What is a win-set? The set of all possible international agreements that would win approval from the necessary domestic constituents if put to an up-or-down vote. Agreement is possible only where the win-sets of the negotiating parties overlap.
Is a small win-set good or bad for a negotiator? Both. A small win-set can strengthen a negotiator's hand because the other side knows he or she cannot concede much. But it also makes overlap less likely and raises the risk that talks fail or that an agreement is not ratified.
What is involuntary defection? When a negotiator who intends to keep an agreement cannot do so because the domestic ratification process fails. Putnam distinguished this from voluntary defection, which is deliberate cheating.
Does "ratification" mean a parliamentary vote? Not necessarily. Putnam used the term for any domestic process needed to endorse or implement an agreement, including the cooperation of unions, bureaucracies or public opinion.
What event inspired the theory? Putnam's research on the 1978 Bonn summit of Western economic powers, where Germany, Japan and the United States each agreed to policy changes that a domestic minority already favored but could not achieve without international pressure.
Is two-level game theory a formal mathematical model? Putnam presented it as a metaphor and conceptual framework. Later scholars, including Iida, Mo and Tarar, built formal models based on it.
Sources and further reading
- Wikipedia, "Two-level game theory": https://en.wikipedia.org/wiki/Two-level_game_theory
- Robert D. Putnam, "Diplomacy and Domestic Politics: The Logic of Two-Level Games," International Organization 42(3), 1988. DOI record: https://doi.org/10.1017/s0020818300027697
- Portuguese translation of Putnam's article, "Diplomacia e política doméstica: a lógica dos jogos de dois níveis," Revista de Sociologia e Política 18(36), 2010 (full text, consulted for this article): https://www.redalyc.org/pdf/238/23816091010.pdf
- Leonard J. Schoppa, "Two-level games and bargaining outcomes: why gaiatsu succeeds in Japan in some cases but not others," International Organization 47(3), 1993: https://www.cambridge.org/core/journals/international-organization/article/twolevel-games-and-bargaining-outcomes-why-gaiatsu-succeeds-in-japan-in-some-cases-but-not-others/13CA04B02994CBAFE54718ED87CAE1BB
- Jeffrey W. Knopf, "Beyond Two-Level Games: Domestic–International Interaction in the Intermediate-Range Nuclear Forces Negotiations," International Organization 47(4), 1993: https://www.cambridge.org/core/journals/international-organization/article/beyond-twolevel-games-domesticinternational-interaction-in-the-intermediaterange-nuclear-forces-negotiations/4D39CBB8353FD2168465D1C6D9C56703
- Jongryn Mo, "Domestic Institutions and International Bargaining: The Role of Agent Veto in Two-Level Games," American Political Science Review 89(4), 1995: https://cambridge.org/core/journals/american-political-science-review/article/abs/domestic-institutions-and-international-bargaining-the-role-of-agent-veto-in-twolevel-games/AA2E93AF28A237688A0B118184B79D22