Sequential equilibrium in monotone games: A theory-based analysis of experimental data

Abstract

A monotone game is an extensive-form game with complete information, simultaneous moves and an irreversibility structure on strategies. It captures a variety of situations in which players make partial commitments and allows us to characterize conditions under which equilibria result in socially desirable outcomes. However, since the game has many equilibrium outcomes, the theory lacks predictive power. To produce stronger predictions, one can restrict attention to the set of sequential equilibria, or Markov equilibria, or symmetric equilibria, or pure-strategy equilibria. This paper explores the relationship between equilibrium behavior in a class of monotone games, namely voluntary * This research was supported by the Center for Experimental Social Sciences (C.E.S.S.) and the C. V. Starr Center for Applied Economics at New York University. We thank Tom Palfrey for detailed comments and suggestions. We also thank an associate editor and two anonymous referees for their comments. The paper has benefited from suggestions by the participants of seminars at several universities, the AEA 2007 annual meeting in Chicago, the ESA Asia-Pacific Regional 1 contribution games, and the behavior of human subjects in an experimental setting. We find evidence of both pure-and mixed-strategy equilibria and several key features of the symmetric Markov perfect equilibrium (SMPE) in the data. To judge how well the SMPE fits the data, we estimate a model of Quantal Response Equilibrium (QRE) Palfrey 1995, 1998) and find that the decision rules of the QRE model are qualitatively very similar to the empirical choice probabilities.JEL Classification Numbers: D82, D83, C92.

Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner’s Dilemma

“…Logit equilibrium is a special case of quantal response equilibrium (McKelvey and Palfrey, 1995) and extends to dynamic games as "Markov logit equilibrium" (as defined in Breitmoser et al, 2010). Logit equilibrium has been shown to explain experimental observations in many circumstances, including the centipede game (Fey et al, 1996), traveler's dilemma (Capra et al, 1999), auctions (Goeree et al, 2002b), public goods games (Goeree et al, 2002a), monotone contribution games (Choi et al, 2008), and beauty contests (Breitmoser, 2012). Thus, it is a plausible starting point for explaining behavior also in repeated games.…”

Dynamic Contributions to a Public Project: The Impact of Rising Marginal Benefit and Completion Benefits

“…5 Other studies that use a repeating simultaneous dynamic design are Choi et.al. (2008) [7], Battaglini et al (2016) [8], and Gachter et al (2017) [9]. 6 A rising marginal benefit of contribution as a project nears completion would also be consistent with the warm giving hypothesis of Andreoni (1989) [10] because later contributions could be viewed by contributors as more likely to influence whether others will be able to enjoy a completed project.…”

“…A completion benefit exists for any project in which its benefits are not fully experienced until the project is completed. 7 Completion benefits are akin to provision point public goods, where Nash Equilibria exist, which fund public good up to the provision point, in addition to the no-provision complete free-riding case (see Palfrey and Rosenthal, 1984 [12]; Marks and Croson, 1998 [13]; Croson and Marks, 2000 [14]). 4 The model of Compte and Jehiel (2004) [5] provides similar conclusions about how contributions can be enhanced in dynamic funding environments.…”

Voluntary contributions by consent or dissent

“…Logit equilibrium, originally defined by Palfrey (1995, 1998), cannot explain this behavior in dissent games-unlike their fit in threshold monotone games as observed by Choi et al (2008). We examine alternative explanations such as lack of equilibration (level-k reasoning) and violations of IIA (hierarchical reasoning) formalized as nested logit equilibrium (NLE).…”

“…mutual logit response. Choi et al (2008) have shown that logit equilibrium reflects strategic choice in their monotone games fairly well. Since logit equilibria…”