
on Game Theory 
Issue of 2013‒09‒24
thirteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Bettina Klaus 
Abstract:  For marriage markets with equal numbers of men and women and where all men find all women acceptable and all women find all men acceptable, Sasaki and Toda (1992) characterize the core by anonymity, Pareto optimality, consistency, and converse consistency. In a recent paper, Nizamogullari and ÖzkalSanver (2012) generalize this result to the full domain of marriage markets by adding individual rationality and by replacing anonymity with gender fairness. We generalize both results by characterizing the core on the domain of no odd rings roommate markets by individual rationality, anonymity, Pareto optimality, consistency, and converse consistency. We also prove that extending this characterization to the domain of solvable roommate markets is not possible. 
Keywords:  Converse Consistency; Core; Marriage and Roommate Markets 
JEL:  C78 D63 
Date:  2013–09 
URL:  http://d.repec.org/n?u=RePEc:lau:crdeep:13.12&r=gth 
By:  Herbert Hamers; Flip Klijn; Marco Slikker 
Abstract:  Scheduling jobs of decentralized decision makers that are in competition will usually lead to cost inefficiencies. This cost inefficiency is studied using the Price of Anarchy (PoA), i.e., the ratio between the worst Nash equilibrium cost and the cost attained at the centralized optimum. First, we provide a tight upperbound for the PoA that depends on the number of machines involved. Second, we show that it is impossible to design a scheduledbased coordinating mechanism in which a Nash equilibrium enforces the centralized or first best optimum. Finally, by simulations we illustrate that on average the PoA is relatively small with respect to the established tight upperbound. 
Keywords:  sequencing situations, outsourcing, first best solution, game theory, price of anarchy, coordinating mechanism 
JEL:  C72 D82 
Date:  2013–08 
URL:  http://d.repec.org/n?u=RePEc:bge:wpaper:709&r=gth 
By:  BRITZ, Volker (ETH Zürich, Switzerland); HERINGS, JeanJacques (Maastricht University, The Netherlands; Université catholique de Louvain, CORE, B1348 LouvainlaNeuve, Belgium.); PREDTETCHINSKI, Arkadi (Maastricht University, The Netherlands) 
Abstract:  We consider a non–cooperative multilateral bargaining game and study an action–dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector–becomes–proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player, though equilibrium acceptance sets do depend on these probabilities. Next we consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized and equilibrium payoffs are in general Pareto inefficient. Otherwise, equilibrium proposals of all players converge to a weighted Nash Bargaining Solution, where the weights are determined by the probability to propose conditional on a rejection. 
Keywords:  strategic bargaining, subgame perfect equilibrium, stationary strategies, Nash bargaining solution 
JEL:  C78 
Date:  2013–09–11 
URL:  http://d.repec.org/n?u=RePEc:cor:louvco:2013044&r=gth 
By:  Gudmundsson, Jens (Department of Economics, Lund University); Habis, Helga (Department of Economics, Lund University) 
Abstract:  We introduce externalities into a twosided, onetoone assignment game by letting the values generated by pairs depend on the behavior of the other agents. Extending the notion of blocking to this setup is not straightforward; a pair has to take into account the possible reaction of the residual agents to be able to assess the value it could achieve. We define blocking in a rather general way that allows for many behavioral considerations or beliefs. The main result of the paper is that a stable outcome in an assignment game with externalities always exists if and only if all pairs are pessimistic regarding the others' reaction following a deviation. The relationship of stability and optimality is also discussed, as is the structure of the set of stable outcomes. 
Keywords:  Twosided matching; assignment game; externalities; stability 
JEL:  C71 C78 D62 
Date:  2013–08–27 
URL:  http://d.repec.org/n?u=RePEc:hhs:lunewp:2013_027&r=gth 
By:  Haiqing Xu (Department of Economics, Texas University) 
Abstract:  This paper focuses on the identification and estimation of static games of incomplete information with correlated types. Instead of making the (conditional) independence assumption on players' types to simplify the equilibria set, I establish a method that allows to identify subsets of the space of covariates (i.e. publicly observed state variables in payoff functions), for which there exists a unique Bayesian Nash Equilibrium (BNE) and the equilibrium strategies are monotone functions. The unique monotone pure strategy BNE can be characterized in a simple manner, based on which I propose an estimation procedure exploiting the information contained in the subset of the covariate space, and establish the consistency and the limiting distribution of the estimator. 
Keywords:  Incomplete Information Game, Monotone Pure Strategy BNE, Maximum Likelihood Estimation 
JEL:  C35 C62 C72 
URL:  http://d.repec.org/n?u=RePEc:tex:wpaper:130909&r=gth 
By:  Vigeral, Guillaume 
Abstract:  We give an example of a zerosum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the nstage game does not converge as n goes to infinity. 
Keywords:  Compact action sets; Uniform value; Asymptotic behavior; Zero sum stochastic games; 
JEL:  C73 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:ner:dauphi:urn:hdl:123456789/10880&r=gth 
By:  Kenju Kamei; Louis Putterman 
Abstract:  Previous research has shown that opportunities for twosided partner choice in finitely repeated social dilemma games can promote cooperation through a combination of sorting and opportunistic signaling, with late period defections by selfish players causing an endgame decline. How such experience would affect play of subsequent finitelyrepeated games remains unclear. In each of six treatments that vary the cooperation premium and the informational basis for reputation formation, we let sets of subjects play sequences of finitelyrepeated voluntary contribution games to study the competing forces of (a) learning about the benefits of reputation, and (b) learning about backward unraveling. We find, inter alia, that with a high cooperation premium and good information, investment in reputation grows across sets of finitelyrepeated games. 
Keywords:  cooperation, reputation, voluntary contribution, public goods, sorting, endogenous grouping, group formation, experiment 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:bro:econwp:20138&r=gth 
By:  Anderson, Simon P; Erkal, Nisvan; Piccinin, Daniel 
Abstract:  We use cumulative reaction functions to compare longrun market structures in aggregative oligopoly games. We first compile an IO toolkit for aggregative games. We show strong neutrality properties across market structures. The aggregator stays the same, despite changes in the number of firms and their actions. The IIA property of demands (CES and logit) implies that consumer surplus depends on the aggregator alone, and that the Bertrand pricing game is aggregative. We link together the following results: merging parties' profits fall but consumer surplus is unchanged, Stackelberg leadership raises welfare, monopolistic competition is the market structure with the highest surplus. 
Keywords:  aggregative games; contests; Cournot; entry; IIA property; leadership; Logit/CES; mergers; monopolistic competition; oligopoly theory; R&D; strategic substitutes and complements 
JEL:  D43 L13 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9511&r=gth 
By:  Dirk Bergemann; Stephen Morris 
Date:  2013–09–19 
URL:  http://d.repec.org/n?u=RePEc:cla:levarc:786969000000000725&r=gth 
By:  Bhaskar, Venkataraman 
Abstract:  We examine buyer strategic power in the model of dynamic BertrandEdgeworth competition. Two sellers with a limited inventory sell to a single buyer, who has a consumption opportunity in each period. The market power of the sellers is offset by the strategic power of the buyer. By not consuming in any period, the buyer can destroy a unit of demand, thereby intensifying future price competition. If transactions are publicly observed, we find that that a strategic buyer can do significantly better than nonstrategic buyers; strategic power may also give rise to inefficiencies. However, if an agent only perfectly observes those transactions in which he is directly involved, and imperfectly observes other transactions, the strategic power of the buyer is reduced, and in some cases, may be completely eliminated. This highlights the sharp discontinuity between the equilibrium outcomes between perfect and imperfect monitoring. 
Keywords:  BertrandEdgeworth competition; dynamic games; imperfect monitoring; strategic buyer 
JEL:  D43 D92 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9526&r=gth 
By:  Hoppe, Eva I; Schmitz, Patrick W 
Abstract:  In the basic adverse selection model, a seller makes a contract offer to a privately informed buyer. A fundamental hypothesis of incentive theory is that the seller may want to offer a menu of contracts to separate the buyer types. In the good state of nature, total surplus is not different from the symmetric information benchmark, while in the bad state, private information may be welfarereducing. We have conducted a laboratory experiment with 954 participants to test these hypotheses. While the results largely corroborate the theoretical predictions, we also find that private information may be welfareenhancing in the good state. 
Keywords:  Incentive theory; Laboratory experiment; Mechanism design; Private information 
JEL:  C72 C92 D82 D86 
Date:  2013–06 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9510&r=gth 
By:  de Clippel, Geoffroy; Eliaz, Kfir; Rozen, Kareen 
Abstract:  Consumers purchase multiple types of goods and services, but may be able to examine only a limited number of markets for the best price. We propose a simple model which captures these features, conveying some new insights. A firm's price can deflect or draw attention to its market, and consequently, limited attention introduces a new dimension of competition across markets. We fully characterize the resulting equilibrium, and show that the presence of partially attentive consumers improves consumer welfare as a whole. When consumers are less attentive, they are more likely to miss the best offer in each market; but the enhanced crossmarket competition decreases average price paid, as leading firms try to stay under the consumers' radar. 
Keywords:  Limited attention 
JEL:  C72 D43 
Date:  2013–07 
URL:  http://d.repec.org/n?u=RePEc:cpr:ceprdp:9553&r=gth 
By:  Choy, James (Department of Economics, University of Warwick) 
Abstract:  Many societies are divided into multiple smaller groups. The defining feature of these groups is that certain kinds of interaction are more likely to take place within a group than across groups. I build a model in which group divisions are enforced through a reputational penalty for interacting with members of different groups. Agents who interact with members of different groups find that they can support lower levels of cooperation in the future. The model explains why agents may be punished by the other members of their group for interacting with members of different groups and why agents are punished for interacting with members of some groups but not others. I test the empirical implication that there should be less cooperation among members of groups that make up a larger percentage of their communities. I discuss the origin and possible future of social division. JEL classification: Cooperation ; Caste ; Social Institution JEL codes: C7 ; O12 ; O17 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:wrk:warwec:1011&r=gth 