
on Game Theory 
By:  Alan F. Breardon; Colin Rowat 
Abstract:  It is known that, in onegood pillage games, stable sets are finite. For m goods, it has been conjectured that the stable sets have measure zero. We introduce a class of sets, termed pseudoindifference sets, which includes level sets of utility functions, quasiindifference classes associated with a preference relation not given by a utility function, production possibility frontiers, and Pareto efficient sets. We establish the truth of the conjecture by proving that pseudoindifference sets in Rp have pdimensional measure zero. This implies that stable sets in nagent, mgood pillage games have m(n  1)dimensional measure zero. We then prove that each pseudoindifference set in Rp has Hausdorff dimension at most p  1, a much stronger result than measure zero. Finally, we establish a stronger version of the conjecture: stable sets in nagent, mgood pillage games have dimension at most m(n1)1. 
Keywords:  pillage games, cooperative game theory, stable sets, Hausdorff dimension 
JEL:  C71 D51 P14 
Date:  2010–02 
URL:  http://d.repec.org/n?u=RePEc:bir:birmec:1005&r=gth 
By:  Jordi Massó; Alejandro Neme 
Abstract:  We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Setwise stability and Core. We first establish that the Setwise stable set is contained in the Core and it contains the nonempty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Setwise stable set of a twofold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff. 
Keywords:  Assignment game; Core; Setwise stability; Competitive equilibrium. 
JEL:  C78 D78 
Date:  2010–03–05 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:810.10&r=gth 
By:  Daniel Jaume; Jordi Massó; Alejandro Neme 
Abstract:  A multiplepartners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium. 
Keywords:  Matching; Assignment Game; Indivisible Goods; Competitive Equilibrium; Lattice. 
JEL:  C78 D78 
Date:  2010–03–05 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:808.10&r=gth 
By:  Jordi Massó; Inés Moreno de Barreda 
Abstract:  We characterize the class of strategyproof social choice functions on the domain of symmetric singlepeaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategyproof and topsonly social choice functions on the domain of singlepeaked preferences characterized by Moulin (1980)) since, under the domain of symmetric singlepeaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategyproof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design nononto social choice functions to deal with feasibility constraints. 
Keywords:  Strategyproofness, Singlepeaked Preferences, Median Voter, Feasibility Constraints. 
JEL:  D7 
Date:  2010–03–05 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:809.10&r=gth 
By:  Yan Dolinsky 
Abstract:  In this paper we consider Dynkin's games with payoffs which are functions of an underlying process. Assuming extended weak convergence of underlying processes $\{S^{(n)}\}_{n=0}^\infty$ to a limit process $S$ we prove convegence Dynkin's games values corresponding to $\{S^{(n)}\}_{n=0}^\infty$ to the Dynkin's game value corresponding to $S$. We use these results to approximate game options prices with path dependent payoffs in continuous time models by a sequence of game options prices in discrete time models which can be calculated by dynamical programming algorithms. In comparison to previous papers we work under more general convergence of underlying processes, as well as weaker conditions on the payoffs. 
Date:  2009–08 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:0908.3661&r=gth 
By:  A. Arrighetti; S. Curatolo 
Abstract:  In the real world, many social and economic interactions are highly affected by coordination problems. These, in turn, emerge from the trial to dynamically organize strategies of collective action in complex contexts where agents and groups are heterogeneous and information is only imperfectly transmitted. In such an environment, rational strategies of coordination games cannot be set exante because, even if benefits from collective coordination are common knowledge, yet there exist many unknown expost costs to be sustained. Agentbased simulations done in this paper show how these costs impact the net payoff in different stages of the game with different weights depending on structure of the environment and nature of coplayers. With perfect information, coordination is the outcome of the game, as game theory predicts. On the contrary, if coordination costs are positive, coordination failures frequently emerge, even in absence of opportunism (as postulated in this paper). Moreover, our simulations show that information costs are more important, in determining the success of coordination, than both organization and supervision costs. Finally, a new kind of coordination failure can emerge from the dynamic interaction among agents even in contexts where exante gross payoffs are sufficiently high. 
Keywords:  Coordination Games, Agentbased Models, Coordination Costs 
JEL:  B4 C15 C71 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:par:dipeco:2010ep01&r=gth 
By:  Britz Volker (METEOR) 
Abstract:  Two impatient players bargain about the division of a pie under a standard bargaining protocol in discrete time with timeinvariant recognition probabilities. Instantaneous utility is linear, but players discount the future by a constant factor. Before bargaining starts, a player can commit to a utility level. This commitment is perfectly binding initially. However, once so much time has passed that even receiving the entire pie would yield less than thecommitted level of utility, then the commitment becomes void. Intuitively, this simply means that no player can remain committed to something which has become impossible. If only one player can commit, his subgameperfect equilibrium payoff varies between one half and the entire pie, depending on the distribution of proposal power. If both players commit sequentially before the bargaining starts, we find a unique perfect equilibrium division. If both players commit simultaneously, there is a range of perfect equilibrium divisions. However, no player obtains less than one third of the pie, even with arbitrarily small proposal power. The equal split is the only division supported by a perfect equilibrium for any choice of the discount factor and the recognition probabilities. 
Keywords:  microeconomics ; 
Date:  2010 
URL:  http://d.repec.org/n?u=RePEc:dgr:umamet:2010013&r=gth 
By:  Gustavo Bergantiños; Jordi Massó; Alejandro Neme 
Abstract:  The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with singlepeaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are singlepeaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation. 
Keywords:  Division Problem, Singlepeaked Preferences, Uniform Rule, Voluntary Participation 
JEL:  D71 
Date:  2010–03–05 
URL:  http://d.repec.org/n?u=RePEc:aub:autbar:807.10&r=gth 