
on Game Theory 
Issue of 2011‒02‒05
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Pierpaolo Battigalli; Alfredo Di Tillio; Dov Samet 
Abstract:  Interactive epistemology in dynamic games studies forms of strategic reasoning like backward and forward induction by means of a formal representation of players’ beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. Strategies are conjunctions of behavioral conditionals of the form “if history h occurred, then player i would choose action ai.” In this literature, strategies are literally interpreted as (objective) behavioral conditionals. But the intutitive interpretation of "strategy" is that of (subjective) "contingent plan of action." As players do not delegate their moves to devices that mechanically execute a strategy, plans cannot be anything but beliefs of players about their own behavior. In this paper we analyze strategic reasoning in dynamic games with perfect information by means of epistemic models where states of the world describe the actual play path (not behavioral conditionals) and the players' conditional probability systems about the path and about each other conditional beliefs. Therefore, the players' beliefs include their contingent plans. We define rational planing as a property of beliefs, whereas material consistency connects plans with choices on the actual play path. Material rationality is the conjunction of rational planning and material consistency. In perfect information games of depth two (the simplest dynamic games), correct belief in material rationality only implies a Nash outcome, not the backward induction one. We have to consider stronger assumptions of persistence of belief in material rationality in order to obtain backward and forward induction reasoning. 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:375&r=gth 
By:  Aristotelis Boukouras (GeorgAugustUniversity Göttingen); Kostas Koufopoulos (University of Warwick) 
Abstract:  We consider a general economy, where agents have private information about their types. Types can be multidimensional and potentially interdependent. We show that, if the interim distribution of types is common knowledge (the exact number of agents for each type is known), then a mechanism exists, which is consistent with truthful revelation of private information and which implements firstbest allocations of resources as the unique BayesNash equilibrium. Our result requires weak restrictions on preferences (Local NonCommon Indifference Property) and on the Pareto correspondence (Anonymity) and it is robust to small perturbations regarding the knowledge of the interim distribution. Our paper is useful in understanding the power of information aggregation in alleviating incentive constraints and is particularly pertinent to games with large populations, in which case the interim distribution of types converges to a unique distribution. 
Keywords:  adverse selection; anonymity; firstbest allocations; full implementation; information aggregation; mechanism design; singlecrossing property; Pareto correspondence 
JEL:  D71 D82 D86 
Date:  2011–01–20 
URL:  http://d.repec.org/n?u=RePEc:got:gotcrc:062&r=gth 
By:  Anat Bracha; Donald J. Brown 
Abstract:  Optimism bias is inconsistent with the independence of decision weights and payoffs found in models of choice under risk, such as expected utility theory and prospect theory. Hence, to explain the evidence suggesting that agents are optimistically biased, we propose an alternative model of risky choice, affective decision making, where decision weights—which we label affective or perceived risk—are endogenized. Affective decision making (ADM) is a strategic model of choice under risk where we posit two cognitive processes—the "rational" and the "emotional" process. The two processes interact in a simultaneousmove intrapersonal potential game, and observed choice is the result of a pure Nash equilibrium strategy in this game. We show that regular ADM potential games have an odd number of locally unique pure strategy Nash equilibria, and demonstrate this finding for ADM in insurance markets. We prove that ADM potential games are refutable by axiomatizing the ADM potential maximizers. 
Keywords:  Insurance 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:fip:fedbwp:1016&r=gth 
By:  Tsubota, Kenmei; Kawasaki, Yujiro 
Abstract:  We examine network formation via bilateral trade agreement (BTA) among three symmetric countries. Each government decides whether to form a link or not via a BTA depending on the differential of expost and exante sum of real wages in the country. We model the governmental decision in two forms, myopic and farsighted and analyze the effects on the BTA network formation. Firstl, we find that both myopic and farsighted games never induce the formation of star networks nor empty networks. Second, the networks resulting from myopic game coincides with those resulting from farsighted games. 
Keywords:  International trade, International agreements, Trade policy, Endogenous network formation, Bilateral trade agreement, Myopic and farsighted behavior 
JEL:  F14 F15 
Date:  2011–01 
URL:  http://d.repec.org/n?u=RePEc:jet:dpaper:dpaper274&r=gth 
By:  Reinoud Joosten; Robin Meijboom 
Abstract:  We introduce a stochastic game in which transition probabilities depend on the history of the play, i.e., the playersâ€™ past action choices. To solve this new type of game under the limiting average reward criterion, we determine the set of jointlyconvergent purestrategy rewards which can be supported by equilibria involving threats. We examine the following setting for motivational and expository purposes. Each period, two agents exploiting a fishery choose between catching with restraint or without. The fish stock is in either of two states, High or Low, and in the latter each action pair yields lower payoffs. Restraint is harmless to the fish, but it is a dominated strategy in each stage game. Absence of restraint damages the resource, i.e., the less restraint the agents show, the higher the probabilities that Low occurs at the next stage of the play. This state may even become â€˜absorbingâ€™, i.e., transitions to High become impossible. 
Keywords:  Stochastic games, endogenous transitions, limiting average rewards, equilibria, common pool resource dilemma Length 29 pages 
JEL:  C72 C73 Q22 Q57 
Date:  2010–11–25 
URL:  http://d.repec.org/n?u=RePEc:esi:evopap:201024&r=gth 
By:  Noemí Navarro (Departement d’Économique et GREDI, Université de Sherbrooke); Andrés Perea (Department of Quantitative Economics, Maastricht University) 
Abstract:  We consider situations where the cooperation and negotiation possibilities between pairs of agents are given by an undirected graph. Every connected component of agents has a value, which is the total surplus the agents can generate by working together. We present a simple, sequential, bilateral bargaining procedure, in which at every stage the two agents in a link (i, j) bargain about their share from cooperation in the connected component they are part of. We show that, if the marginal value of a link is increasing in the number of links in the connected component it belongs to, then this procedure yields exactly the Myerson value payoff (Myerson, 1977) for every player. 
Keywords:  Myerson value, networks, bargaining, cooperation 
JEL:  C71 C72 
Date:  2010–11–15 
URL:  http://d.repec.org/n?u=RePEc:shr:wpaper:1029&r=gth 
By:  Alp Atakan; Mehmet Ekmekci 
Abstract:  In a twosided search market agents are paired to bargain over a unit surplus. The matching market serves as an endogenous outside option for agents in a bargaining relationship. Behavioral agents are (strategically inflexible) commitment types that demand a constant portion of the unit surplus. The steady state frequency of behavioral types in the market is determined in equilibrium. We show, even if behavioral types are negligible, they substantially effect the terms of trade and efficiency. In an unbalanced market where the entering flow of one side is short, bargaining follows equilibrium play in a bargaining game with onesided reputation, the terms of trade are determined by the commitment types on the short side, and commitment types improve efficiency. In a balanced market where the entering flows of the two sides are equal, bargaining follows equilibrium play in a bargaining game with twosided reputation and commitment types cause inefficiency. An inefficient equilibrium with persistent delays and breakups is constructed. The magnitude of inefficiency is determined by the inflexible demands of the commitment types and is independent of the fraction of the commitment types entering the market. 
Keywords:  Bargaining, Reputation, Search, Dynamic Matching, WarofAttrition. JEL Classification Numbers: C78, D83 
Date:  2010–01 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1508&r=gth 
By:  Nicolas Quérou; Raphael Soubeyran 
Abstract:  In this paper, we consider a model of multilateral bargaining where homogeneous agents may exert e¤ort before negotiations in order to inuence their chances to become the proposer. E¤ort levels have a permanent effect on the recognition process (persistent recognition). We prove two main results. First, all voting rules are equivalent (that is, they yield the same social cost) when recognition becomes persistent. Secondly, an equilibrium may fail to exist, because players may have more incentives to reduce their e¤ort level (in order to be included in winning coalitions) than to increase it (in order to increase their proposal power). Both results di¤er greatly from the case where recognition is transitory: Yildirim (2007) shows that una nimity is the unique strictly optimal rule, and that an equilibrium always exists (under mild assumptions) in such a setting. Moreover, our second conclusion is quite di¤erent from the one obtained in most of the existing literature on bargaining (which assumes an exogenous recognition process), where it is generally considered that it is always in an agents best interest to have a proposal power as high as possible. 
Date:  2011–01 
URL:  http://d.repec.org/n?u=RePEc:lam:wpaper:0411&r=gth 
By:  Nikhil Vellodi (University of Warwick) 
Abstract:  In this paper, we generalize the notion of a communication equilibrium (Forges 1986, Myerson 1986) of a game with incomplete information by introducing two new types of correlation device, namely extended and Bayesian devices. These new devices explicitly model the `thinking process' of the device, i.e. the manner in which it generates outputs conditional on inputs. We proceed to endow these devices with both information processing errors, in the form of nonpartitional information, and multiple transition and prior distributions, and prove that these two properties are equivalent in this context, thereby generalizing the result of Brandenburger, Dekel and Geanakoplos (1988). We proceed to discuss the Revelation Principle for each device, and conclude by nesting a certain class of `cheaptalk' equilibria of the underlying game within Bayesian communication equilibria. These socalled fallible talk equilibria cannot be generated by standard communication equilibria. 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:955&r=gth 
By:  Pierpaolo Battigalli; Andrea Prestipino 
Abstract:  We analyze forwardinduction reasoning in games with asymmetric information under the assumption that some given restrictions ? on players’initial or conditional firstorder beliefs are "transparent", that is, not only the restrictions ? hold, but there is common belief in ? at every node. Most applied models of asymmetric information are covered as special cases whereby ? pins down the probabilities initially assigned to states of nature. But the abstract analysis also allows for transparent restrictions on beliefs about behavior, e.g. independence restrictions or restrictions induced by the context behind the game. Our contribution is twofold. First, we study the differences and similarities between two versions of extensive form rationalizability incorporating such restrictions: strong ?rationalizability (Battigalli [3, 1999], [4, 2003]) and ?rationalizability (BattigalliSiniscalchi [11, 2003]). Second, we provide an epistemic characterization for the former solution concept, showing that it is the conceptually correct one. This is compared with an alternative characterization due to BattigalliSiniscalchi [12, 2007] whereby the ?restrictions are not assumed to be transparent, but rather to have the same "epistemic priority" as the rationality assumption. 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:igi:igierp:376&r=gth 
By:  JeanChristophe PEREAU (GREThA, UMR CNRS 5113); Sébastien ROUILLON (GREThA, UMR CNRS 5113) 
Abstract:  This article analyses the bargaining side of the Coase theorem in a 3player strategic framework. We consider several bilateral bargaining protocols between two firms polluting one household (the victim). Our results show that when property rights are given to the victim, he prefers to bargain separetely and simultaneously with the two firms. However when property rights are given to the firms, they prefer to bargain sequentially with the household. This last configuration yields a non optimal outcome and invalidates the bargaining Coase theorem. 
Keywords:  Coase theorem, delegation, non cooperative bargaining, property rights, sequential negotiation, simultaneous negotiation 
JEL:  C78 K41 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:grt:wpegrt:201102&r=gth 
By:  Wioletta Dziuda; Antoine Loeper 
Abstract:  This paper analyzes an ongoing bargaining situation in which i) preferences evolve overtime, ii) the interests of individuals are not perfectly aligned, and iii) the previous agreement becomes the next status quo and determines the payoffs until a new agreement is reached. We show that the endogeneity of the status quo exacerbates the players’ conflict of interest and decreases the responsiveness of the bargaining outcome to the environment. Players with arbitrarily similar preferences can behave as if their interests were highly discordant. When players become very patient, the endogeneity of the status quo can bring the negotiations to a complete gridlock. Under mild regularity conditions, fixing the status quo throughout the game via an automatic sunset provision improves welfare. The detrimental effect of the endogeneity of the status quo can also be mitigated by concentrating decision rights, for instance, by lowering the supermajority requirement. 
Keywords:  Dynamic voting, endogenous status quo, supermajority, partisanship, polarization, policy inertia, sunset provision JEL Classification Numbers: C73, D72, D78 
Date:  2010–10–26 
URL:  http://d.repec.org/n?u=RePEc:nwu:cmsems:1514&r=gth 
By:  Börner, Lars; Quint, Daniel 
Abstract:  This paper studies the market microstructure of preindustrial Europe. In particular we investigate the institution of the broker in markets and fairs, and develop a unique data set of approximately 1100 sets of brokerage rules in 42 merchant towns in Central and Western Europe from the late 13th to the end of the 17th century. We show that towns implemented brokerage as an efficient matchmaking institution in a twosided market problem. Furthermore, towns differentiated sellerfriendly from buyerfriendlier matching mechanisms. We show that the decision to implement matchmaking mechanisms, and whether these mechanisms would be buyer or seller friendly, depends on the products in question and the stated policy goals of the town, as well as time and geographic variables.  
Keywords:  preindustrial markets,market microstructure,efficient matching 
JEL:  D4 N23 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:zbw:fubsbe:201031&r=gth 
By:  Francisco MartínezMora; M. Socorro Puy 
Abstract:  We introduce two natural types of asymmetric singlepeaked preferences, which we name biasedabove and biasedbelow, depending on whether the asymmetry (or preferencebias) favors alternatives above or below the peak. We define a rich family of utility functions, the generalized distancemetric utility functions, that can represent preferences biasedabove or biasedbelow, besides accommodating any degree of asymmetry. We also identify restrictions on differentiable utility representations that guarantee the underlying preferences to be biasedabove or below, and allow to compare degrees of asymmetry. Finally, we consider a specific application agents preferences over government size to illustrate the role of factors such as risk aversion and tax distortions in shaping asymmetric preferences. 
Date:  2011–01 
URL:  http://d.repec.org/n?u=RePEc:fda:fdaddt:201103&r=gth 
By:  Sujoy Chakravarty; Carine Sebi; E. Somanathan; E. Theophilus 
Abstract:  The public goods problem (Hardin, The Tragedy of the Commons,1968), either viewed as a problem of extraction and optimal use of a resource, or that of shared contributions to the cost of a resource, has had a long history in the social sciences. Our experimental design, using methods in experimental economics, uses a standard Voluntary Contributions Mechanism (VCM) game with a moderately large group of ten and facetoface communication between the participants. The subjects, who are villagers in the GoriGanga Basin of the Central Himalayas, are not rematched every period. Our results are somewhat different from laboratory experiments using a similar design such as Isaac and Walker (1988a, 1988b). [Occasional paper 29]. 
Keywords:  communication, participants, VCM, economics, public goods problems, INDIAN HIMALAYAS, villagers, resource, goriganga, social sciences 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:ess:wpaper:id:3490&r=gth 
By:  Burkhard, Schipper (University of California Davis) 
Abstract:  We develop awarenessdependent subjective expected utility by taking unawareness structures introduced in Heifetz, Meier, and Schipper (2006, 2008, 2009) as primitives in the AnscombeAumann approach to subjective expected utility. We observe that a decision maker is unaware of an event if and only if her choices reveal that the event is "null" and the negation of the event is "null". Moreover, we characterize "impersonal" expected utility that is behaviorally indistinguishable from awarenessdependent subject expected utility and assigns probability zero to some subsets of states that are not necessarily events. We discuss in what sense probability zero can model unawareness. 
JEL:  C70 C72 D80 D81 
Date:  2010–12 
URL:  http://d.repec.org/n?u=RePEc:ecl:ucdeco:1022&r=gth 