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Robert D. Putnam employs the metaphor of a two-level game to discuss international relationships and domestic politics. To do so he borrows the language of game theory. Terms such as "strategy," "win," "loss," "payoffs," "rules," and "choices" populate the text. Negotiators at the international Level I table engage in a delicate balancing act. Any moves made at Level I must be ratified at the domestic Level II where groups vie for political advantage. Level I negotiators know that any agreement arranged internationally can be rejected at home. Strategizing becomes a key feature of the role that chief negotiators play in international discussions.
Negotiators with a larger set of potential agreements with domestic approval or "win-sets" have an advantage in striking satisfactory deals. Putnam explains that Level II advantages can sometimes turn into disadvantages at Level I. He notes that "the larger the perceived win-set of a negotiator, the more he can be 'pushed around' by other Level I negotiators." Consistency between moves made at each table is key. Putnam describes inconsistency as costly because some policy changes must either be adopted or not. What happens in practice will affect everyone involved.
Like board games international negotiations always involve uncertainty. Players look to minimize uncertainty and maximize their chances of winning. Chief negotiators at Level I represent teams of bureaucratic agencies, interest groups, social classes, and other constituents from Level II. The pressure is high when the status quo is domestically unpalatable. Negotiators who stand to gain from striking agreements have less room to determine the terms of the agreement.
Putnam defines win-sets as "the set of all possible Level I agreements that would 'win.'" An agreement must be ratified among domestic constituents without amendments to "win." Domestic agreement processes are varied. Wherever smaller margins are needed, agreements are more likely. Putnam offers the example of the U.S. Senate, in which endorsements of a proposed agreement must receive a vote of at least two-thirds to be ratified. This makes approval in the U.S. more challenging than in places where only a simple majority is needed for ratification. The difficulties of achieving ratification at Level II can turn into bargaining strengths at Level I.
Agreements eligible for approval at Level I will by definition fall within the range of overlapping win-sets. Figure 1 illustrates this requirement. Agreements are expected where win-sets are large. Smaller win-sets generally cause more uncertainty. There is often a risk that a negotiator with a small win-set will be forced to quit the discussions. It is in the interest of each negotiator to act to expand the win-sets of each party at Level I. This is not always easy to accomplish because domestic constituents can be difficult to influence. Nonetheless negotiators should take any steps that they can to help get the potential agreements approved.
The sizes of win-sets are determined in part by negotiation strategies. Ratification procedures also influence the sizes of win-sets. When a simple majority is needed for ratification, win-sets are typically larger. Each group of players faces a unique distribution of power, and power dynamics affect the sizes of win-sets. Groups that stand to benefit from an agreement are going to put more pressure on negotiators to strike a deal. On the other hand, groups satisfied with the status quo are unlikely to be motivated to encourage the negotiator to reach an agreement. Putnam illustrates this idea with a labor example. "Members of two-wage-earner families should be readier to strike ... than sole breadwinners," he writes. In cases in which the only domestic dispute centers around the palatability of a "no agreement" outcome, the domestic interests are called "homogeneous." The negotiator's task in homogenous disputes is to be certain that they win as much as is possible at Level I. Where a domestic dispute is multifaceted or "heterogeneous," the negotiator faces a challenging balancing act. Putnam says this is what happened to Germany at the Bonn summit, and a transnational alignment between Germany and Italy emerged as a result. Putnam writes that "in such cases, domestic divisions may improve the prospects for international cooperation." Domestic strife can sometimes give birth to new transnational alignments.