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on Game Theory |
| By: | Vincent Anesi (Kennedy School of Government, Harvard University) |
| Abstract: | This note studies the noncooperative foundations of von Neumann- Morgenstern (vN-M) stable sets in voting games. To do so, we study Markov perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following result emerges from such an exercise: Every stable set of the underlying simple game is the limit set of undominated Markov perfect equilibria of the bargaining game, which form a strategically stable set of equilibria, when voters are suciently farsighted; thus establishing a relationship between vN-M stability and strategic stability in voting games. |
| Keywords: | Legislative bargaining, committee, strategic stability, stable set. |
| JEL: | C71 C78 D71 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2007-09&r=gth |
| By: | Aziz, Haris (Computer Science Department, University of Warwick); Paterson, Mike (Computer Science Department, University of Warwick); Leech, Dennis (Economics Department, University of Warwick) |
| Abstract: | Weighted voting games are ubiquitous mathematical models which are used in economics, political science, neuroscience, threshold logic, reliability theory and distributed systems. They model situations where agents with variable voting weight vote in favour of or against a decision. A coalition of agents is winning if and only if the sum of weights of the coalition exceeds or equals a specified quota. We provide a mathematical and computational characterization of multiple weighted voting games which are an extension of weighted voting games1. We analyse the structure of multiple weighted voting games and some of their combinatorial properties especially with respect to dictatorship, veto power, dummy players and Banzhaf indices. Among other results we extend the concept of amplitude to multiple weighted voting games. An illustrative Mathematica program to compute voting power properties of multiple weighted voting games is also provided. |
| Keywords: | multi-agent systems ; multiple weighted ; voting games ; game theory, algorithms and ; complexity ; voting power. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:823&r=gth |
| By: | Csóka Péter; Herings P. Jean-Jacques; Kóczy László Á, (METEOR) |
| Abstract: | The measurement and the allocation of risk are fundamental problems of portfolio management. Coherent measures of risk provide an axiomatic approach to the former problem. In an environment given by a coherent measure of risk and the various portfolios’ realization vectors, risk allocation games aim at solving the second problem: How to distribute the diversification benefits of the various portfolios? Understanding these cooperative games helps us to find stable, efficient, and fair allocations of risk. We show that the class of risk allocation and totally balanced games coincide hence a stable allocation of risk is always possible. When the aggregate portfolio is riskless: risk is limited to subportfolios, the class of risk allocation games coincides with the class of exact games. As in exact games any subcoalition may be subject to marginalization even in core allocations, our result further emphasizes the responsibility in allocating risk. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007040&r=gth |
| By: | Csóka Péter; Herings P. Jean-Jacques; Kóczy László Á. (METEOR) |
| Abstract: | We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another. |
| Keywords: | operations research and management science; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007039&r=gth |
| By: | López-Pérez, Raúl (Departamento de Análisis Económico (Teoría e Historia Económica). Universidad Autónoma de Madrid.) |
| Abstract: | In games with multiple equilibria, the fairest equilibrium –in case one exists- may be the obvious solution for some players but not for others, and players can be aware of this heterogeneity. This paper theoretically explores how coordination could be achieved in this case. The model is consistent with abundant experimental evidence and explains, for instance, why (a) the attractiveness of the fair equilibrium, (b) out-of-equilibrium payoffs, (c) dominated strategies, and (d) the number of players and available strategies matter for coordination. The model is compared with alternative equilibrium selection criteria like risk and payoff dominance and ideas for new experiments are suggested. |
| Keywords: | Coordination; Equilibrium Refinement; Fairness; Focal Points; Heterogeneity |
| JEL: | C72 D02 D62 D64 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:uam:wpaper:200714&r=gth |
| By: | Ondrej Rydval (Max Planck Institute of Economics, Jena, Germany, and CERGE-EI); Andreas Ortmann (CERGE-EI, Charles University Prague and Academy of Sciences of the Czech Republic); Michal Ostatnicky (CERGE-EI, Charles University Prague and Academy of Sciences of the Czech Republic) |
| Abstract: | We study the nature of dominance violations in three minimalist dominance-solvable guessing games, featuring two or three players choosing among two or three strategies. We examine how subjects' reported reasoning translates into their choices and beliefs about others' choices, and how reasoning and choices relate to their measured cognitive and personality characteristics. Only about a third of our subjects reason in accord with dominance; they always make dominant choices and almost always expect others to do so. By contrast, around 60% of subjects describe reasoning processes inconsistent with dominance, yet a quarter of them actually make dominant choices and a fifth of them expect others to do so. Dominance violations seem to arise mainly due to subjects misrepresenting the strategic nature of the guessing games. Reasoning errors are more likely for subjects with lower ability to maintain and allocate attention, as measured by working memory, and for subjects with weaker intrinsic motivation and premeditation attitudes. |
| Keywords: | cognition, bounded rationality, beliefs, guessing games, experiment |
| JEL: | C72 C92 D83 |
| Date: | 2007–11–21 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-092&r=gth |
| By: | Predtetchinski Arkadi (METEOR) |
| Abstract: | We study a model of multilateral bargaining over social outcomes represented by points in the unit interval. An acceptance or rejection of a proposal is determined by a voting rule as represented by a collection of decisive coalitions. The focus of the paper is on the asymptotic behavior of subgame perfect equilibria in stationary strategies as the discount factor goes to one. We show that, along any sequence of stationary subgame perfect equilibria, as the discount factor goes to one, the social acceptance set collapses to a point. This point, called the bargaining outcome, is independent of the sequence of equilibria and is uniquely determined by the set of players, the utility functions, the recognition probabilities, and the voting rule. The central result of the paper is a characterization of the bargaining outcome as a unique zero of the characteristic equation. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007045&r=gth |
| By: | Herings P. Jean-Jacques; Predtetchinski Arkadi (METEOR) |
| Abstract: | We study a process of bargaining over social outcomes represented by points in theunit interval. The identity of the proposer is determined by a general Markov process and the acceptance of a proposal requires the approval of it by all the players. We show that for every value of the discount factor below one the subgame perfect equilibrium in stationary strategies is essentially unique and equal to what we call the bargaining equilibrium. We provide a general characterization of the bargaining equilibrium. We consider next the asymptotic behavior of the equilibrium proposals when the discount factor approaches one. We give a complete characterization of the limit of the equilibrium proposals. We show that the limit equilibrium proposals of all the players are the same if the proposer selection process satisfies an irreducibility condition, or more generally, has a unique absorbing set. In general, the limit equilibrium proposals depend on the partition of the set of players in absorbing sets and transient states of the proposer selection process. We fully characterize the limit equilibrium proposals as the unique generalized fixed point of a particular function.This function depends in a simple way on the stationary distribution related to the proposer selection process. We compare the proposal selected according to our bargaining model to the one corresponding to the median voter theorem. |
| Keywords: | microeconomics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007044&r=gth |
| By: | Bochet Olivier; Klaus Bettina (METEOR) |
| Abstract: | We discuss a problem concerning Dasgupta, Hammond, and Maskin''s (1979) definition of a rich domain and a very well-known result they established for these domains: on rich domains, if a social choice function is implementable in Nash strategies, then it is truthfully implementable in dominant strategies Dasgupta, Hammond, and Maskin''s (1979, Theorem 7.2.3). This result is cited many times in later papers, e.g., Laffont and MaskinL(1982, Theorem 4) and Maskin (1985, Theorem 7). Dasgupta, Hammond, and Maskin''s (1979) proof of this result essentially is based on showing that (Maskin) monotonicity implies strategy-proofness (or equivalently independent person-by-person monotonicity IPM).In the sequel we abbreviate Dasgupta, Hammond, and Maskin (1979) by DHM. We describe DHM''s model in Section 2.In Section 3 we first construct an example of a DHM rich domain and a social choice function that is monotonic but not strategy-proof (Example 1). This suggests that DHM''s rich domain definition is not sufficient to show that monotonicity implies strategy-proofness (or that Nash implementability implies truthful implementability in dominant strategies). We then investigate which step in DHM''s proof is problematic - since DHM do not give a direct proof of the result, we reproduce Maskin’s (1985) proof. In Section 4, we consider the presentation of Dasgupta, Hammond, and Maskin''s (1979) definition of a rich domain in the Maskin and Sjöström (2002). It turns out that there definition of a rich domain is different from DHM''s original definition. With this adjusted richness condition the proof that monotonicity implies strategy-proofness is correct. |
| Keywords: | Economics ; |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2007041&r=gth |
| By: | Alan Mehlenbacher (Department of Economics, University of Victoria) |
| Abstract: | This study uses a multiagent system to investigate how sealed-bid auction results vary across twodimensional value signals from pure private to pure common value. I find that several auction outcomes are significantly nonlinear across the two-dimensional value signals. As the common value percent increases, profit, revenue, and efficiency all decrease monotonically, but they decrease in different ways. Finally, I find that forcing revelation by the auction winner of the true common value may have beneficial revenue effects when the common-value percent is high and there is a high degree of uncertainty about the common value. |
| Keywords: | Axiomatic bargaining, resource monotonicity, transferable utility, risk aversion; Agent-based computational economics, multi-dimensional value signals, sealed-bid auctions, impulse balance learning |
| JEL: | C71 D13 D63 C15 C72 D83 |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicddp:0707&r=gth |
| By: | Alan Mehlenbacher (Department of Economics, University of Victoria) |
| Abstract: | This study uses a multiagent system to investigate English auctions with two-dimensional value signals and agents that learn a signal-averaging factor. I find that signal averaging increases nonlinearly as the common value percent increases, decreases with the number of bidders, and decreases at high common value percents when the common value signal is more uncertain. Using signal averaging, agents increase their profit when the value is more uncertain. The most obvious effect of signal averaging is on reducing the percentage of auctions won by bidders with the highest common value signal. |
| Keywords: | Axiomatic bargaining, resource monotonicity, transferable utility, risk aversion; Agent-based computational economics, multi-dimensional value signals, English auctions, signal averaging |
| JEL: | C71 D13 D63 C15 C72 D83 |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicddp:0708&r=gth |
| By: | Alan Mehlenbacher (Department of Economics, University of Victoria) |
| Abstract: | This study uses a multiagent system to determine which payment rule provides the most revenue in Treasury auctions that are based on Canadian rules. The model encompasses the when-issued, auction, and secondary markets, as well as constraints for primary dealers. I find that the Spanish payment rule is revenue inferior to the Discriminatory payment rule across all market price spreads, but the Average rule is revenue superior. For most market-price spreads, Uniform payment results in less revenue than Discriminatory, but there are many cases in which Vickrey payment produces more revenue. |
| Keywords: | Axiomatic bargaining, resource monotonicity, transferable utility, risk aversion; Agent-based computational economics, treasury auctions, auction context |
| JEL: | C71 D13 D63 C15 C72 D83 |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicddp:0709&r=gth |
| By: | Alan Mehlenbacher (Department of Economics, University of Victoria) |
| Abstract: | I have developed a multiagent system platform that provides a valuable complement to the alternative auction research methods. The platform facilitates the development of heterogeneous agents and provides an experimental environment that is under the experimenter's complete control. Simulations with alternative learning methods results in impulse balance learning as the most promising approach for auctions. |
| Keywords: | Axiomatic bargaining, resource monotonicity, transferable utility, risk aversion; Agent-based computational economics, agent learning |
| JEL: | C71 D13 D63 C15 C72 D83 |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:vic:vicddp:0706&r=gth |
| By: | Kumagai, Satoru |
| Abstract: | Researchers have long believed the concept of “excitement†in games to be subjective and difficult to measure. This paper presents the development of a mathematically computable index that measures this concept from the viewpoint of an audience. One of the key aspects of the index is the differential of the probability of “winning†before and after one specific “play†in a given game. If the probability of winning becomes very positive or negative by that play, then the audience will feel the game to be “exciting.†The index makes a large contribution to the study of games and enables researchers to compare and analyze the “excitement†of various games. It may be applied to many fields especially the area of welfare economics, ranging from allocative efficiency to axioms of justice and equity. |
| Keywords: | Game, Game system, Excitement, Mathematics |
| JEL: | C69 D63 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:jet:dpaper:dpaper121&r=gth |
| By: | Ciftci, B.B.; Tijs, S.H. (Tilburg University, Center for Economic Research) |
| Abstract: | In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost sharing where each player pays the edge which he chooses in the procedure. The main result of the paper is that the average of the n! cost sharings provided by our procedure is equal to the P-value for minimum cost spanning tree situations introduced and characterized by Branzei et al. (2004). As a side product, we find a new method, the vertex oriented procedure, to construct minimum cost spanning trees. |
| Keywords: | Minimum cost spanning tree games;algorithm;value;cost sharing. |
| JEL: | C71 D72 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200789&r=gth |
| By: | Brams, Steven J.; Kilgour, D. Marc |
| Abstract: | Three models are presented in which two players agree to share power in a particular ratio, but either player may subsequently “fire” at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the agreement stays in place; if one is successful, that player obtains all the power; if each eliminates the other, both players get nothing. In Model I, the game is played once, and in Model II it is repeated, with discounting of future payoffs. Although there are conditions under which each player would prefer not to shoot, satisfying these conditions for one player precludes satisfying them for the other, so at least one player will always have an incentive to shoot. In anticipation, its rival would prefer to shoot, too, so there will be a race to preempt. In Model III, a damage factor caused by shooting, whether successful or not, is introduced into Model II. This mitigates the incentive to shoot but does not eliminate it entirely. The application of the models to conflicts, especially civil wars, is discussed. |
| Keywords: | power sharing; repeated game; duel; civil wars |
| JEL: | D74 C72 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5769&r=gth |
| By: | Brams, Steven J.; Kilgour, D. Marc |
| Abstract: | Power sharing is modeled as a duel over some prize. Each of two players may either share the prize in some ratio or fire at the other player—either in sequence or simultaneously—and eliminate it with a specified probability. If one player eliminates the other without being eliminated itself, it captures the entire prize, but the prize is damaged over time when there is shooting. Simultaneous shooting, which is more damaging than sequential shooting, tends to induce the players to share the prize and expand their opportunities for sharing it. It was effectively implemented by the superpowers with the doctrine of “launch on warning” during the Cold War, and it was strengthened by the development of second-strike capability. Deterring terrorism has proved a different matter, because terrorists are difficult to detect and present few targets that can be damaged. |
| Keywords: | power sharing; game; duel; deterrence; terrorism |
| JEL: | D74 C7 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5771&r=gth |
| By: | Pierre-Andre Chiappori; Robert McCann (Institute for Fiscal Studies and University of Toronto); Lars Nesheim (Institute for Fiscal Studies) |
| Abstract: | <p><p><p><p>Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match. An appendix resolves an old problem (# 111) of Birkhoff in probability and statistics [5], by giving a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all joint measures with the same marginals.</p></p></p></p></p></p></p> |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:ifs:cemmap:23/07&r=gth |