
on Game Theory 
By:  Rene Saran (Brown University); Roberto Serrano (Brown University & IMDEA) 
Abstract:  We apply stochastic stability to study the evolution of bidding behavior in privatevalues secondprice, firstprice and kdouble auctions. The learning process has a strong component of inertia but with a small probability, the bids are modified in the direction of expost regrets. We identify essentially a unique bid that will be used by each type in the long run. In the secondprice auction, this is the truthful bid. In the firstprice auction, bidding half of one’s valuation is stable. The stable bid in the kdouble auction is a toughening of the ChatterjeeSamuelson linear equilibrium strategy. If we add a friction in changing one’s bid, then truthtelling behavior is also obtained in the firstprice and kdouble auctions. Intuitively, the stochastically stable bid minimizes the maximal regret. 
Keywords:  stochastic stability; expost regret; secondprice auction; firstprice auction; kdouble auction 
JEL:  C73 C78 D44 D83 
Date:  2007–04–10 
URL:  http://d.repec.org/n?u=RePEc:imd:wpaper:wp200710&r=gth 
By:  Hayley Chouinard; Jonathan Yoder (School of Economic Sciences, Washington State University) 
Abstract:  This paper characterizes a set of Nash equilibria in a firstprice sealedbid auction with the right of first refusal using two bidders and asymmetric information regarding the bidders’ value distributions. The equilibria for multiple bidders and a more general value distribution are also presented 
Keywords:  repeated auction; right of first refusal; asymmetric information 
JEL:  C72 D44 D82 
Date:  2006–06 
URL:  http://d.repec.org/n?u=RePEc:wsu:wpaper:chouinard1&r=gth 
By:  Thomas W.L. Norman 
Abstract:  The Folk Theorem for infinitely repeated games offers an embarrassment of riches; nowhere is equilibrium multiplicity more acute. This paper selects amongst these equilibria in the following sense. If players learn to play an infinitely repeated game using classical hypothesis testing, it is known that their strategies almost always approximate equilibria of the repeated game. It is shown here that if, in addition, they are sufficiently "conservative" in adopting their hypotheses, then almost all of the time is spent approximating an efficient subset of equilibria that share a "forgiving" property. This result provides theoretical justification for the general sense amongst practitioners that efficiency is focal in such games. 
Keywords:  Repeated Games, Folk Theorem, Learning, Hypothesis Testing, Equilibrium Selection 
JEL:  C72 C12 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:296&r=gth 
By:  H. Peyton Young 
Abstract:  The paper surveys recent work on learning in games and delineates the boundary between forms of learning that lead to Nash equilibrium and forms that lead to weaker notions of equiibrium (or none at all). 
Keywords:  Equilibrium, Learning, Dynamics 
JEL:  C7 D83 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:304&r=gth 
By:  Thomas W.L. Norman 
Abstract:  This paper demonstrates that inertia driven by switching costs leads to more rapid evolution in a class of games that includes m x m pure coordination games. Under the bestresponse dynamic and a fixed rate of mutation, the expected waiting time to reach longrun equilibrium is of lower order in the presence of switching costs, due to the creation of new absorbing "inertia" states that allow Ellison`s (Review of Economic Studies 67, 2000, 1745) "stepbystep" evolution to occur. 
Keywords:  Evolution, Mutations, Longrun Equilibrium, Waiting Times, Inertia, Switching Costs 
JEL:  C72 C73 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:299&r=gth 
By:  Pivato, Marcus 
Abstract:  Given a bargaining problem, the `relative utilitarian' (RU) solution maximizes the sum total of the bargainer's utilities, after having first renormalized each utility function to range from zero to one. We show that RU is `optimal' in two very different senses. First, RU is the maximal element (over the set of all bargaining solutions) under any partial ordering which satisfies certain axioms of fairness and consistency; this result is closely analogous to the result of Segal (2000). Second, RU offers each person the maximum expected utility amongst all rescalinginvariant solutions, when it is applied to a random sequence of future bargaining problems which are generated using a certain class of distributions; this is somewhat reminiscent of the results of Harsanyi (1953) and Karni (1998). 
Keywords:  relative utilitarian; bargaining solution; impartial observer 
JEL:  D63 D71 
Date:  2007–04–09 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:2637&r=gth 
By:  Matthias Kräkel (Department of Economics, BWL II, University of Bonn, Adenauerallee 2442, D53113 Bonn. Tel: +49228739211, Fax: +49228739210, Germany, email: m.kraekel@unibonn.de) 
Abstract:  We analyze the optimal choice of risk in a twostage tournament game between two players that have different concave utility functions. At the first stage, both players simultaneously choose risk. At the second stage, both observe overall risk and simultaneously decide on effort or investment. The results show that those two effects which mainly determine risk taking — an effort effect and a likelihood effect — are strictly interrelated. This finding sharply contrasts with existing results on risk taking in tournament games with symmetric equilibrium efforts where such linkage can never arise. Hence, previous findings based on symmetry at the effort stage turn out to be nongeneric. 
Keywords:  asymmetric equilibria, rankorder tournaments, risk taking 
JEL:  C72 J3 L1 M5 
Date:  2007–04 
URL:  http://d.repec.org/n?u=RePEc:trf:wpaper:200&r=gth 
By:  Rafael HortalaVallve 
Abstract:  Can we devise mechanisms that allow voters to express the intensity of their preferences when monetary transfers are forbidden? Would we then be able to take account of how much voters wish the approval or dismissal of any particular issue? In such cases, would some minorities be able to decide over those issues they feel very strongly about? As opposed to the classical voting system (one person  one decision  one vote), we propose a new voting system where each agent is endowed with a fixed number of votes that can be distributed freely between a predetermined number of issues that must be approved or dismissed. Its novelty relies on allowing voters to express the intensity of their preferences in a simple manner. This voting system is optimal in a welldefined sense: in a setting with two voters, two issues and preference intensities uniformly and independently distributed across possible values, Qualitative Voting Pareto dominates Majority Rule and, moreover, achieves the only exante optimal (incentive compatible) allocation. The result also holds true with three voters as long as the voters preferences towards the issue differ sufficiently. 
Keywords:  Voting, Intensity Problem, Alternatives to Majority Rule, Conflict Resolution 
JEL:  C72 D70 P16 
Date:  2007 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:320&r=gth 
By:  Martin Browing; PierreAndre Chiappori; Valerie Lechene 
Abstract:  We derive distributional effects for a noncooperative alternative to the unitary model of household behaviour. We consider the Nash equilibria of a voluntary contributions to public goods game. Our main result is that, in general, the two partners either choose to contribute to different public goods or they contribute to at most one common good. The former case coresponds to the separate spheres case of Lundberg and Pollak (1993). The second outcome yields (local) income pooling. A household will be in different regimes depending on the distribution of income within the household. Any bargaining model with this noncooperative case as a breakdown point will inherit the local income pooling. We conclude that targeting benefits such as child benefits to one household member may not always have an effect on outcomes. 
Keywords:  Nash Equilibrium, Nash Bargaining, Collective Models, IntraHousehold Allocation 
JEL:  D10 C71 C72 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:293&r=gth 
By:  Martin Browing; PierreAndre Chiappori; Valerie Lechene 
Abstract:  Allocations familiales et autres transferts cibles sont generalement verses aux meres, sur la base de l`observation qu`augmenter la part des ressources controlees par les meres conduit a ameliorer le bienetre des enfants. Nous recensons un ensemble de resultats empiriques qui etablisent le bienfonde de ces mesures. Nous contrastons ensuite les predictions theoriques des principales alternatives au modele standard de comportement des menages, le modele unitaire. Ceci permet d`etablir que l`effet predit des transferts depend des preferences individuelles et du pouvoir des membres du menage, mais aussi crucialement de la forme des interactions dans le menage. 
Keywords:  Transferts Cibles, Equilibre de Nash, Modele Collectif, Solution de Nash, Allocation IntraFamiliale, Mise en Commun des Ressources, Spheres Separees 
JEL:  D10 C71 C72 
Date:  2006 
URL:  http://d.repec.org/n?u=RePEc:oxf:wpaper:294&r=gth 