
on Game Theory 
Issue of 2011‒06‒18
fourteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Helga Habis (Institute of Economics  Hungarian Academy of Sciences); P. JeanJacques Herings (Department of Economics, Universiteit Maastricht) 
Abstract:  We introduce the concept of a TUUgame, a transferable utility game with uncertainty. In a TUUgame there is uncertainty regarding the payoffs of coalitions. One out of a finite number of states of nature materializes and conditional on the state, the players are involved in a particular transferable utility game. We consider the case without ex ante commitment possibilities and propose the Weak Sequential Core as a solution concept. We characterize the Weak Sequential Core and show that it is nonempty if all ex post TUgames are convex. 
Keywords:  transferable utility games, uncertainty, Weak Sequential Core 
JEL:  C71 C73 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1120&r=gth 
By:  Timo Hiller (European University Institute) 
Abstract:  This paper presents a gametheoretic model of network formation, which allows agents to enter bilateral alliances and to extract payoffs from enemies. Each pair of agents creates a surplus of one, which allies divide in equal parts. If agents are enemies, then the agent with more allies obtains a larger share of the surplus. I show that Nash equilibria are of two types. First, a state of utopia, where all agents are allies. Second, asymmetric equilibria, such that agents can be partitioned into sets of different size, where agents within the same set are allies and agents in different sets are enemies. These results stand in contrast to coalition formation games in the economics of conflict literature, where stable group structures are generally symmetric. The model provides a gametheoretic foundation for structural balance, a long standing notion in social psychology, which has been fruitfully applied to the study of alliance formation in international relations. 
Keywords:  Network Formation, Economics of Conflict, Contest Success Function, Structural Balance, International Relations 
JEL:  D86 D74 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2011.42&r=gth 
By:  Pelosse, Yohan 
Abstract:  This paper introduces a notion of partitioned correlated equilibrium that extends Aumann's correlated equilibrium concept (1974, 1987). This concept captures the noncooperative interactions arising simultaneously within and between groups. We build on this notion in order to provide a foundation for contest success functions (CSFs) in a game wherein contests arise endogenously. Our solution concept and analysis are general enough to give a foundation for any model of contest using standard equilibrium concepts like e.g., Nash, BayesianNash or PerfectNash equilibria. In our environment, popular CSFs can be interpreted as a list of equilibrium conjectures held by players whenever they contemplate deviating from the ``peaceful outcome'' of the ``group formation game''. Our setup allows to relate the form of prominent CSFs with some textbook examples of quasilinear utility functions, social utility functions in the spirit of Fehr and Schmidt (1999) and nonexpected models of utility a la Quiggin (1981, 1982). We also show that our framework can accommodate situations in which agents cannot correlate their actions. 
Keywords:  Contest success functions; Correlated equilibrium; Inter and intragroup conflicts; Induced contests 
JEL:  D74 C72 
Date:  2011 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:31468&r=gth 
By:  Peter Csoka (Institute of Economics  Hungarian Academy of Sciences); Miklos Pinter (Department of Mathematics  Corvinus University of Budapest) 
Abstract:  Measuring and allocating risk properly are crucial for performance evaluation and internal capital allocation of portfolios held by banks, insurance companies, investment funds and other entities subject to financial risk. We show that by using coherent measures of risk it is impossible to allocate risk satisfying the natural requirements of (Solution) Core Compatibility, Equal Treatment Property and Strong Monotonicity. To obtain the result we characterize the Shapley value on the class of totally balanced games and also on the class of exact games. Our result can also be seen as a downside of coherent measures of risk. 
Keywords:  Coherent Measures of Risk, Risk Allocation Games, Totally Balanced Games, Exact Games, Shapley value, Solution core 
JEL:  C71 G10 
Date:  2011–04 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1117&r=gth 
By:  Julia Belau 
Abstract:  In this paper, I introduce an extension of (TU) games with a coalition structure. Taking a situation where all coalitions are already established is not reasonable in order to forecast the reality; there is not only one possible coalition, there are several. I consider situations where coalitions are not established yet and take into account the likelihood of each possible coalition. This leads to a generalized, probabilistic setting for coalition structures. Probabilistic versions of known axioms are introduced as well as new probabilistic axioms. Generalizations of both the outsideoptionsensitive chivalue (Casajus, Soc Choice Welf 32, 113, 2009) and its outsideoptioninsensitive pendant, the component restricted Shapley value (Aumann and Drèze, Int. J. Game Theory 3, 217237, 1974), are defined and axiomatic characterizations are given. 
Keywords:  TU game; coalition structure; outside option 
JEL:  C71 
Date:  2011–01 
URL:  http://d.repec.org/n?u=RePEc:rwi:repape:0236&r=gth 
By:  Tam s Fleiner (Budapest University of Economics and Technology  Department of Computer Science and Information Theory); Bal zs Sziklai (Institute of Economics  Hungarian Academy of Sciences) 
Abstract:  We offer a new approach to the wellknown bankruptcy problem based on Kaminski's idea. With the help of hydraulic rationing we give a proof to Aumann and Maschlers theorem i.e. the consistent solution of a bankruptcy problem is the nucleolus of the corresponding game. We use a system of vessels and water and the principles of mechanics to show this fact. The proof is not just simple and demonstrative but also provides an insight how the nucleolus is constructed in such games. 
Keywords:  bankruptcy problem, nucleolus, hydraulic rationing 
JEL:  C71 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1123&r=gth 
By:  Arnold Polanski (School of Economics, University of East Anglia); Emiliya A. Lazarova (University of Birmingham) 
Abstract:  We study dynamic multilateral markets, in which players’ payoffs result from coalitional bargaining. In this setting, we establish payoff uniqueness of the stationary equilibria when players exhibit some degree of impatience. We focus on market games with different player types, and derive under mild conditions an explicit formula for each type’s equilibrium payoff as market frictions vanish. The limit payoff of a type depends in an intuitive way on the supply and the demand for this type in the market, adjusted by the typespecific bargaining power. Our framework may be viewed as an alternative to the Walrasian pricesetting mechanism. When we apply this methodology to the analysis of labor markets, we can determine endogenously the equilibrium firm size and remuneration scheme. We find that each worker type in a stationary market equilibrium is rewarded her marginal product, i.e. we obtain a strategic underpinning of the neoclassical wage. Interestingly, we can also replicate some standardized facts from the searchtheoretical literature such as positive equilibrium unemployment. 
Keywords:  Multilateral Bargaining, Dynamic Markets, Labor Markets 
JEL:  C71 C72 C78 J30 L20 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2011.44&r=gth 
By:  Florian M. Biermann (The Hebrew University of Jerusalem) 
Abstract:  In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly “disruptive” subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: the subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison. 
Keywords:  Stable Marriage Problem, Matching, Blocking Pair, Instability, Matching Comparison, Decentralized Market, Bargaining Set 
JEL:  C0 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2011.41&r=gth 
By:  Narayanan, Sridhar (Stanford University) 
Abstract:  Discrete games of complete information have been used to analyze a variety of contexts such as market entry, technology adoption and peer effects. They are extensions of discrete choice models, where payoffs of each player are dependent on actions of other players, and each outcome is modeled as Nash equilibria of a game, where the players share common knowledge about the payoffs of all the players in the game. An issue with such games is that they typically have multiple equilibria, leading to the absence of a onetoone mapping between parameters and outcomes. Theory typically has little to say about equilibrium selection in these games. Researchers have therefore had to make simplifying assumptions, either analyzing outcomes that do not have multiplicity, or making adhoc assumptions about equilibrium selection. Another approach has been to use a bounds approach to set identify rather than point identify the parameters. A third approach has been to empirically estimate the equilibrium selection rule. In this paper, we take a Bayesian MCMC approach to estimate the parameters of the payoff functions in such games. Instead of making adhoc assumptions on equilibrium selection, we specify a prior over the possible equilibria, reflecting the analyst's uncertainty about equilibrium selection and find posterior estimates for the parameters that accounts for this uncertainty. We develop a sampler using the reversible jump algorithm to navigate the parameter space corresponding to multiple equilibria and obtain posterior draws whose marginal distributions are potentially multimodal. When the equilibria are not identified, it goes beyond the bounds approach by providing posterior distributions of parameters, which may be important given that there are likely regions of low density for the parameters within the bounds. When data allow us to identify the equilibrium, our approach generates posterior estimates of the probability of specific equilibria, jointly with the estimates for the parameters. Our approach can also be cast in a hierarchical framework, allowing not just for heterogeneity in parameters, but also in equilibrium selection. Thus, it complements and extends the existing literature on dealing with multiplicity in discrete games. We first demonstrate the methodology using simulated data, exploring the methodology in depth. We then present two empirical applications, one in the context of joint consumption, using a dataset of casino visit decisions by married couples, and the second in the context of market entry by competing chains in the retail stationery market. We show the importance of accounting for multiple equilibria in these application, and demonstrate how inferences can be distorted by making the typically used equilibrium selection assumptions. Our applications show that it is important for empirical researchers to take the issue of multiplicity of equilibria seriously, and that taking an empirical approach to the issue, such as the one we have demonstrated, can be very useful. 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:ecl:stabus:2079&r=gth 
By:  Sunghoon Hong (Vanderbilt University) 
Abstract:  We develop a strategic model of network interdiction in a noncooperative game of flow. An adversary, endowed with a bounded quantity of bads, chooses a flow specifying a plan for carrying bads through a network from a base to a target. Simultaneously, an agency chooses a blockage specifying a plan for blocking the transport of bads through arcs in the network. The bads carried to the target cause a target loss while the blocked arcs cause a network loss. The adversary earns and the agency loses from both target loss and network loss. The adversary incurs the expense of carrying bads. In this model we study Nash equilibria and find a power law relation between the probability and the extent of the target loss. Our model contributes to the literature of game theory by introducing noncooperative behavior into a KalaiZemel (cooperative) game of flow. Our research also advances models and results on network interdiction. 
Keywords:  Network Interdiction, Noncooperative Game of Flow, Nash Equilibrium, Power Law, KalaiZemel Game of Flow 
JEL:  C72 D85 H56 
Date:  2011–06 
URL:  http://d.repec.org/n?u=RePEc:fem:femwpa:2011.43&r=gth 
By:  Nizar Allouch (Queen Mary, University of London  Department of Economics); Monique Florenzano (CES  Centre d'économie de la Sorbonne  CNRS : UMR8174  Université PanthéonSorbonne  Paris I, EEPPSE  Ecole d'Économie de Paris  Paris School of Economics  Ecole d'Économie de Paris) 
Abstract:  For an exchange economy, under assumptions which did not bring about the existence of quasiequilibrium with dividends as yet, we prove the nonemptiness of the fuzzy rejective core. Then, via Konovalov (1998, 2005)'s equivalence result, we solve the equilibrium (with dividends) existence problem. In a last section, we show the existence of a Walrasian quasiequilibrium under a weak nonsatiation condition which differs from the weak nonsatiation assumption introduced by AllouchLe Van (2009). This result, designed for exchange economies whose consumers' utility functions are not assumed to be upper semicontinuous, complements the one obtained by MartinsdaRocha and Monteiro (2009). 
Keywords:  Exchange economy, satiation, equilibrium with dividends, rejective core, fuzzy rejective core, core equivalence. 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:hal:cesptp:halshs00598038&r=gth 
By:  Helga Habis (Institute of Economics  Hungarian Academy of Sciences); P. JeanJacques Herings (Department of Economics, Universiteit Maastricht) 
Abstract:  We examine the notion of the core when cooperation takes place in a setting with time and uncertainty. We do so in a twoperiod general equilibrium setting with incomplete markets. Market incompleteness implies that players cannot make all possible binding commitments regarding their actions at different dateevents. We unify various treatments of dynamic core concepts existing in the literature. This results in definitions of the Classical Core, the Segregated Core, the Twostage Core, the Strong Sequential Core, and the Weak Sequential Core. Except for the Classical Core, all these concepts can be defined by requiring absence of blocking in period 0 and at any dateevent in period 1. The concepts only differ with respect to the notion of blocking in period 0. To evaluate these concepts, we study three market structures in detail: strongly complete markets, incomplete markets in finance economies, and incomplete markets in settings with multiple commodities. Even when markets are strongly complete, the Classical Core is argued not to be an appropriate concept. For the general case of incomplete markets, the Weak Sequential Core is the only concept that does not suffer from major defects. 
Keywords:  Incomplete Markets, Dynamic Core Concepts, Time and uncertainty 
JEL:  C71 C73 D52 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1119&r=gth 
By:  Nikolaos Georgantzís (GLOBE & Department of Economics, University of Granada); Antonios Proestakis (GLOBE & Department of Economics, University of Granada) 
Abstract:  Wealth heterogeneity infuences people's behavior in several socioeconomic environments, especially when groups consisting of "unequal" members have to take a collective action which affects all members equally or proportionally. After eliciting real outoflab wealth, we form 4player groups playing an oneshot public good game with heterogeneous laboratory endowments. Endowing subjects according or against their real wealth gives rise to a series of interesting results. Endowment heterogeneity, lack of real relative wealth information and being "rich" both inside and outside the lab raise contributions. Finally, when eliciting subjects' beliefs, we find out that only relatively "poor" subjects expect others to contribute more than what they actually are prepared to do theirselves. 
Keywords:  Public goods, experiment, endowment heterogeneity, real wealth 
Date:  2011–06–01 
URL:  http://d.repec.org/n?u=RePEc:gra:wpaper:10/20&r=gth 
By:  I. Hasnas; L. Lambertini; A. Palestini 
Abstract:  We analyze an Open Innovation process in a Cournot duopoly using a differential game approach where knowledge spillovers are endogenously determined via the R&D process. The game produces multiple steady states, allowing for an asymmetric solution where a firm may trade off the R&D investment against information absorption from the rival. 
JEL:  C73 L13 O31 
Date:  2011–05 
URL:  http://d.repec.org/n?u=RePEc:bol:bodewp:wp753&r=gth 