
on Game Theory 
Issue of 2013‒10‒18
twentyone papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University 
By:  Vermeulen A.J.; Schröder M.J.W.; Peters H.J.M. (GSBE) 
Abstract:  This paper considers the estate division problem from a noncooperative perspective. The integer claim game initiated by ONeill 1982 and extended by Atlamaz et al. 2011 is generalized by considering different sharing rules to divide every interval among the claimants. For problems with an estate larger than half of the total entitlements, we show that every sharing rule satisfying four fairly general axioms yields the same set of Nash equilibrium profiles and corresponding payoffs. Every rule that always results in such equilibrium payoff vector is characterized by the properties minimal rights first and lower bound of degree half. Wellknown examples are the Talmud rule, the adjusted proportional rule and the random arrival rule. Then our focus turns to more specific claim games, i.e. games that use the constrained equal awards rule, the Talmud rule, or the constrained equal losses rule as a sharing rule. Also a variation on the claim game is considered by allowing for arbitrary instead of integer claims. 
Keywords:  Noncooperative Games; Conflict; Conflict Resolution; Alliances; 
JEL:  C72 D74 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013055&r=gth 
By:  Vermeulen A.J.; Schröder M.J.W.; Peters H.J.M. (GSBE) 
Abstract:  We consider effectivity functions for finitely many players and alternatives. We assume that players have incomplete information with respect to the preferences of the other players. Our main result is the characterization of effectivity functions which have an ex post Nash consistent representation, i.e., there is a game form such that i the distribution of power among coalitions of players is the same as in the effectivity function and ii there is an ex post Nash equilibrium in pure strategiesfor any preference profile. 
Keywords:  Existence and Stability Conditions of Equilibrium; Game Theory and Bargaining Theory: General; Asymmetric and Private Information; Mechanism Design; 
JEL:  C62 C70 D82 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013049&r=gth 
By:  Herings P.J.J.; Csóka P. (GSBE) 
Abstract:  Risk allocation games are cooperative games that are used to attribute the risk of a financial entity to its divisions. In this paper, we extend the literature on risk allocation games by incorporating liquidity considerations. A liquidity policy specifies statedependent liquidity requirements that a portfolio should obey. To comply with the liquidity policy, a financial entity may have to liquidate part of its assets, which is costly. The definition of a risk allocation game under liquidity constraints is not straightforward, since the presence of a liquidity policy leads to externalities. We argue that the standard worst case approach should not be used here and present an alternative definition. We show that the resulting class of transferable utility games coincides with the class of totally balanced games. It follows from our results that also when taking liquidity considerations into account there is always a stable way to allocate 
Keywords:  Cooperative Games; General Financial Markets: General (includes Measurement and Data); 
JEL:  C71 G10 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013057&r=gth 
By:  Peter Biro (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences); Tamas Fleiner (Department of Computer Science and Information Theory, Budapest University of Technology and Economics); Rob Irving (School of Computing Science, University of Glasgow) 
Abstract:  Scarf's algorithm [18] provides fractional core elements for NTUgames. Bir¢ and Fleiner [3] showed that Scarf's algorithm can be extended for capacitated NTUgames. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different intensities up to some limits, and the contribution of the agents can also differ in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called stable allocations. In this paper we apply this solution concept for the Hospitals Residents problem with Couples (HRC). This is one of the most important general stable matching problems due to its relevant applications, also wellknown to be NPhard. We show that if a stable allocation yielded by the Scarf algorithm turns outto be integral then it provides a stable matching for an instance of HRC, so this method can be used as a heuristic. In an experimental study, we compare this method with other heuristics constructed for HRC that are applied in practice in the American and Scottish resident allocation programs, respectively. Our main finding is that the Scarf algorithm outperforms all the other known heuristics when the proportion of couples is high. 
Keywords:  Scarf lemma, stable allocation, hospitals residents problem, couples 
JEL:  C71 C78 
Date:  2013–09 
URL:  http://d.repec.org/n?u=RePEc:has:discpr:1330&r=gth 
By:  Khai Xiang Chiong (Division of the Humanities and Social Sciences, California Institute of Technology) 
Abstract:  This paper proposes a revealed preference test of network formation models. Specifically, I consider network formation models where agents are (1) strategic, (2) externalities are confined to within an agentâ€™s kneighborhood, where k can be varied. I show that this model can be tested using observation of a single network. I then derive necessary and sufficient condition under which the observed network is consistent with our strategic models of network formation. This nonparametric test takes the form of an algorithm involving the computation of colorpreserving automorphisms of graphs. Building on the theoretical result, the test is implemented to calculate itsâ€™ statistical power and to the Banerjee et al. (2012)â€™s social network data. 
Keywords:  Revealed preference, Networks formation, Social networks, Pair wise stability, Model testing, Testable implications, Graph automorphism 
JEL:  C14 C52 C72 D85 
Date:  2013–09 
URL:  http://d.repec.org/n?u=RePEc:net:wpaper:1323&r=gth 
By:  Alexander M. Jakobsen; B. Curtis Eaton (University of Calgary); David Krause 
Abstract:  When agents make their choices simultaneously, network effects often give rise to a selection problem involving perfectly coordinated, Paretooptimal equilibria. We characterize this selection problem, and introduce a generalized sequential choice model to address it. In this model, we show how expectation formation under imperfect information combines with network effects to form coordination cascades: ordered partitions of the agent space wherein coordination on one alternative is eventually optimal for all agents. Several theorems are proven regarding both the likelihood and extent of coordination under various parameter changes; in particular, we show that the degree to which agents can observe the choices of others is an important consideration. We also present numerical calculations which shed additional light on the coordination problem, and which suggest that sequential choice resolves, with high probability, the equilibrium selection problem efficiently. 
Date:  2013–10–11 
URL:  http://d.repec.org/n?u=RePEc:clg:wpaper:200914&r=gth 
By:  Rohan Dutta; Ryosuke Ishii 
Abstract:  An important form of commitment is the ability to restrict the set of future actions from which choices can be made. We study a simple dynamic game of complete information which incorporates this type of commitment. For a given initial game, the players engage in an endogenously determined number of commitment periods before choosing from the remaining actions. We show the existence of equilibria with pure strategies in the commitment periods. For important classes of games, including pure coordination games and the staghunt game the equilibrium outcome is unique and efficient. This is despite the synchronous move structure. Moreover, efficient coordination does not necessarily involve commitments on the equilibrium path: the option alone is sufficient. 
Keywords:  Dynamic Commitment, Endogenous Timing, Coordination Games, Uniqueness, Payoff Dominance, Stag Hunt 
JEL:  C72 C73 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:mtl:montec:102013&r=gth 
By:  Daniele Nosenzo (School of Economics, University of Nottingham); Simone Quercia (School of Economics, University of Nottingham); Martin Sefton (School of Economics, University of Nottingham) 
Abstract:  We study the effect of group size on cooperation in voluntary contribution mechanism games. As in previous experiments, we study four and eightperson groups in high and low marginal per capita return (MPCR) conditions. We find a positive effect of group size in the low MPCR condition, as in previous experiments. However, in the high MPCR condition we observe a negative group size effect. We extend the design to investigate two and threeperson groups in the high MPCR condition, and find that cooperation is highest of all in twoperson groups. The findings in the high MPCR condition are consistent with those from nperson prisoner’s dilemma and oligopoly experiments that suggest it is more difficult to sustain cooperation in larger groups. The findings from the low MPCR condition suggest that this effect can be overridden. In particular, when cooperation is low other factors, such as considerations of the social benefits of contributing (which increase with group size), may dominate any negative group size effect. 
Keywords:  voluntary contribution mechanism, cooperation, group size 
Date:  2013–05 
URL:  http://d.repec.org/n?u=RePEc:not:notcdx:201305&r=gth 
By:  Ke, Changxia 
Abstract:  Alliances often face both freeriding and holdup problems, which under mine the effectiveness of alliances in mobilizing joint fighting effort. Despite of these disadvantages, alliances are still ubiquitous in all types of contests. This paper asks if there are nonmonetary incentives to form alliances, e.g., intimidating/discouraging the single player(s) who is/are left alone. For this purpose, I compare symmetric (2 vs. 2) and asymmetric (2 vs. 1) contests to their equivalent 4player and 3player individual contests, respectively. We find that alliance players in symmetric (2 vs. 2) contests behave the same as those in equivalent 4player individual contests. However, in asymmetric (2 vs. 1) contests, standalone players were strongly discouraged to exert effort (especially the females), compared to the 3player individual contests. Alliance players may have anticipated this effect and also reduced their effort, if alliances share the prize according to the merit rule. Behavioural factors such as the need to belong can help reconcile the "paradox of alliance formation". 
Keywords:  Alliance Formation; Contest and Conflict; Experiment 
JEL:  D72 D74 C91 
Date:  2013–03–12 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:421&r=gth 
By:  Eric Hoffmann (Department of Economics, The University of Kansas) 
Abstract:  Global games methods are aimed at resolving issues of multiplicity of equilibria and coordination failure that arise in game theoretic models by relaxing common knowledge assumptions about an underlying parameter. These methods have recently received a lot of attention when the underlying complete information game is one of strategic complements (GSC). Little has been done in this direction concerning games of strategic substitutes (GSS), however. This paper complements the existing literature in both cases by extending the global games method developed by Carlsson and Van Damme (1993) to Nplayer, multiaction GSS and GSC, using a pdominance condition as the selection criterion. Moreover, this approach is much less restrictive on the conditions that payo_s and the underlying parameter space must satisfy, and therefore serves to cirumvent recent criticisms to global games methods. The second part of this paper generalizes the model by allowing _groups_ of players to receive homogenous signals, which, under certain conditions, strengthens the model's power of predictability. 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:kan:wpaper:201308&r=gth 
By:  Storcken A.J.A.; Peters H.J.M.; Roy S.; Sen A. (GSBE) 
Abstract:  It is proved that every strategyproof, peaksonly or unanimous, probabilistic rule defined over a minimally rich domain of singlepeaked preferences is a probability mixture of strategyproof, peaksonly or unanimous, deterministic rules over the same domain. The proof employs Farkas Lemma and the maxflow mincut theorem for capacitated networks. 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013040&r=gth 
By:  Theodoros M. Diasakos (University of St Andrews); Kostas Koufopoulos 
Abstract:  This paper revisits the problem of adverse selection in the insurance market of Rothschild and Stiglitz (QJE, 1976). We propose a simple extension of the gametheoretic structure in Hellwig (EER, 1987) under which Nashtype strategic interaction between the informed customers and the uninformed firms results always in a particular separating equilibrium. The equilibrium allocation is unique and Paretoefficient in the interim sense subject to incentivecompatibility and individual rationality. In fact, it is the unique neutral optimum in the sense of Myerson (ECMA, 1983). 
Keywords:  Insurance Market, Adverse Selection, Incentive Efficiency 
JEL:  D86 
URL:  http://d.repec.org/n?u=RePEc:san:wpecon:1313&r=gth 
By:  Imhof, Lorens; Kräkel, Matthias 
Abstract:  A standard tournament contract specifies only tournament prizes. If agentsâ€™ performance is measured on a cardinal scale, the principal can complement the tournament contract by a gap which defines the minimum distance by which the best performing agent must beat the second best to receive the winner prize. We analyze a tournament with two risk averse agents. Under unlimited liability, the principal strictly benefits from a gap by partially insuring the agents and thereby reducing labor costs. If the agents are protected by limited liability, the principal sticks to the standard tournament. 
Keywords:  limited liability; moral hazard; risk aversion; tournament; unlimited liability 
JEL:  C72 D86 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:411&r=gth 
By:  Enriqueta Aragones; Dimitrios Xefteris 
Abstract:  We analyze a unidimensional model of twocandidate electoral competition where voters have im perfect information about the candidates' policy proposals, that is, voters cannot observe the exact policy proposals of the candidates but only which candidate offers the most leftist/rightist platform. We assume that candidates are purely office motivated and that one candidate enjoys a valence advan tage over the other. We characterize the unique Sequential Equilibrium in veryweakly undominated strategies of the game. In this equilibrium the behavior of the two candidates tends to maximum extremism, due to the voters' lack of information. But it may converge or diverge depending on the size of the advantage. For small values of the advantage candidates converge to the extreme policy most preferred by the median and for large values of the advantage candidates strategies diverge: each candidate specializes in a different extreme policy. These results are robust to the introduction of a proportion of well informed voters. In this case the degree of extremism decreases when the voters become more informed. 
Keywords:  Downsian model; imperfect information; advantaged candidate; maximum differentiation 
JEL:  D72 
Date:  2013–10–14 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:938.13&r=gth 
By:  Eric Schniter (Economic Science Institute, Chapman University); Roman M. Sheremeta (Department of Economics, Weatherhead School of Management, Case Western Reserve University and the Economic Science Institute); Timothy W. Shields (Argyros School of Business and Economics, Chapman University) 
Abstract:  Many economic interactions are characterized by “all or nothing” action spaces that may limit a demonstrable index of trust and, therefore, the propensity to reciprocate. In two experimental trust games, the action space governing investments was manipulated to examine the effects on investments and reciprocity. In the continuous game the investor could invest any amount between $0 and $10, while in the binary game the investor could invest either $0 or $10. In both games, the trustee received the tripled investment and then could return any amount back to the investor. Investors invested significantly more in the binary game than in the continuous game. However, higher investments in the binary game did not lead to more reciprocity. To the contrary, conditional on investment of $10, on average trustees returned significantly less in the binary game than in the continuous game. 
Keywords:  trust game, signaling, demonstrable index of trust, reciprocity, experiments 
JEL:  C72 C91 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:chu:wpaper:1324&r=gth 
By:  Robert Shupp (Department of Agricultural, Food and Resource Economics, Michigan State University); Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University); David Schmidt (Federal Trade Commission, Bureau of Economics); James Walker (Indiana University, Department of Economics) 
Abstract:  Many resource allocation contests have the property that individuals undertake costly actions to appropriate a potentially divisible resource. We design an experiment to compare individuals’ decisions across three resource allocation contests which are isomorphic under riskneutrality. The results indicate that in aggregate the singleprize contest generates lower expenditures than either the proportionalprize or the multiprize contest. Interestingly, while the aggregate results indicate similar behavior in the proportionalprize and multiprize contests, individual level analysis indicates that the behavior in the singleprize contest is more similar to the behavior in the multiprize contest than in the proportionalprize contest. We also elicit preferences toward risk, ambiguity and losses, and find that while such preferences cannot explain individual behavior in the proportionalprize contest, preferences with regard to losses are predictive of behavior in both the singleprize and multipleprize contests. Therefore, it appears that loss aversion is correlated with behavior in the singleprize and multiprize contests where losses are likely to occur, but not in the proportionalprize contest where losses are unlikely. 
Keywords:  contest, rentseeking, experiments, risk aversion, game theory 
JEL:  C72 C92 D72 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:chu:wpaper:1323&r=gth 
By:  Konrad, Kai A.; Morath, Florian 
Abstract:  This paper considers evolutionarily stable decisions about whether to initiate violent conflict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically confined area, we use Schafferâ€™s (1988) concept of evolutionary stability. We find that players â€˜evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent conflict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are reflected in the equilibrium set of peaceful resource allocations. 
Keywords:  Conflict; Contest; Endogenous fighting; Balance of power; Evolutionary stability 
JEL:  D72 D74 
Date:  2013–04–22 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:418&r=gth 
By:  Peters H.J.M.; Karos D. (GSBE) 
Abstract:  In a mutual control structure agents exercise control over each other. Typical examples occur in the area of corporate governance firms and investment companies exercise mutual control, in particular by owning each others stocks. In this paper we formulate a general model for such situations. There is a fixed set of agents, and a mutual control structure assigns to each subset coalition the subset of agents controlled by that coalition. Such a mutual control structure captures directcontrol. We propose a procedure in order to incorporate indirect control as well if S controls T, and S and T jointly control R, then S controls R indirectly. This way, invariant mutual control structures result. Alternatively, mutual control can be described by vectors of simple games, called simple gamestructures, each simple game describing who controls a certain player, and also those simple games can be updated in order to capture indirect control. We show that both approaches lead to equivalent invariant structures. In the second part of the paper, we axiomatically develop a class of power indices for invariant mutual control structures. We impose four axioms with a plausible interpretation in this framework, which together characterize a broad class of power indices based on dividends resulting both from exercising and from undergoing control. By adding an extra condition a unique power index is singled out. In this index, each player accumulates his ShapleyShubik power index assignments from controlling other players, diminished by the sum of the ShapleyShubik power index assignments to other players controlling him. 
Keywords:  Cooperative Games; Mergers; Acquisitions; Restructuring; Voting; Proxy Contests; Corporate Governance; 
JEL:  C71 G34 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:dgr:umagsb:2013048&r=gth 
By:  Kräkel, Matthias; Szech, Nora; von Bieberstein, Frauke 
Abstract:  External recruiting at least weakly improves the quality of the pool of applicants, but the incentive implications are less clear. Using a contest model, this paper investigates the pure incentive effects of external recruiting. Our results show that if workers are heterogeneous, the opening of a firmâ€™s career system may lead to a homogenization of the pool of contestants and, thus, encourage the firmâ€™s high ability workers to exert more effort. If this positive effect outweighs the discouragement of low ability workers, the firm will benefit from external recruiting. If, however, the discouragement effect dominates the homogenization effect, the firm should disregard external recruiting. In addition, product market competition makes opening of the career system less attractive for a firm since it increases the incentives of its competitorsâ€™ workers and hence strengthens the competitors. 
Keywords:  contest; externalities; recruiting; wage policy. 
JEL:  C72 J2 J3 
Date:  2013 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:414&r=gth 
By:  Herbst, Luisa; Konrad, Kai A.; Morath, Florian 
Abstract:  We study endogenous group formation in tournaments employing experimental threeplayer contests. We find that players in endogenously formed alliances cope better with the moral hazard problem in groups than players who are forced into an alliance. Also, players who are committed to expending effort above average choose to stand alone. If these players are forced to play in an alliance, they invest even more, whereas their coplayers choose lower effort. Anticipation of this exploitation may explain their preference to stand alone. 
Keywords:  Endogenous group formation; contest; conflict; alliance; experiment; moral hazard problem; freeriding; ingroup favoritism 
JEL:  D72 D74 
Date:  2013–04–22 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:419&r=gth 
By:  Jean Guillaume Forand (Department of Economics, University of Waterloo); John Duggan (Department of Economics, University of Rochester) 
Abstract:  We establish existence and continuity properties of equilibria in a model of dynamic elections with a discrete (countable) state space and general policies and preferences. We provide conditions under which there is a representative voter in each state, and we give characterization results in terms of the equilibria of an associated “representative voting game.” When the conditions for these results are not met, we provide examples that uncover new classes of dynamic political failures. 
JEL:  C62 C73 D72 
Date:  2013–10 
URL:  http://d.repec.org/n?u=RePEc:wat:wpaper:1305&r=gth 