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on Game Theory |
| By: | Alejandro Manelli (W. P. Carey School of Business Department of Economics) |
| Abstract: | Any stage-game with infinite choice sets can be approximated by finite games obtained as increasingly finer discretizations of the infinite game. The subgame perfect equilibrium outcomes of the finite games converge to a limit distribution. We prove that (i) if the limit distribution is feasible in the limit game, then it is also a subgame perfect equilibrium outcome of the limit game; and (ii) if the limit distribution prescribes sufficiently diffused behavior for first-stage players, then it is a subgame perfect equilibrium outcome of the limit game. These results are potentially useful in determining the existence of subgame perfect equilibria in applications. As an illustration of this potential, it is shown that the addition of cheap talk to the games considered restores the existence of subgame perfect equilibria. |
| URL: | http://d.repec.org/n?u=RePEc:asu:wpaper:2132859&r=gth |
| By: | Hector Chade (W. P. Carey School of Business Department of Economics); Pavlo Prokopovych (University of Michigan); Lones Smith (University of Michigan) |
| Abstract: | <P>We study infinitely repeated games with observable actions, where players have present-biased (so-called (beta)-(delta)) preferences. We give a two-step procedure to characterize Strotz-Pollak equilibrium payoffs: compute the continuation payoff set using recursive techniques, and use this set to characterize the equilibrium payoff set U(beta,delta). While Strotz-Pollak equilibrium and subgame perfection differ here, the generated paths and payoffs do coincide. <P>We then explore the cost of the present-time bias. Fixing the total present value of 1 util flow, lower (beta) or higher (delta) shrinks the payoff set. Surprisingly, unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set U(beta, delta) is not monotonic in (beta) or (delta). While the set U(beta, delta) is contained in that of a standard repeated game with greater discount factor, the present-time bias precludes any lower bound on U(beta, delta) that would easily generalize the (beta) = 1 folk-theorem. |
| URL: | http://d.repec.org/n?u=RePEc:asu:wpaper:2173938&r=gth |
| By: | Nizar Allouch (Queen Mary, University of London); Arkadi Predtetchinski (Maastricht University) |
| Abstract: | The seminal contribution of Debreu-Scarf (1963) connects the two concepts of core and competitive equilibrium in exchange economies. In effect, their core-equilibrium equivalence result states that, when the set of economic agents is replicated, the set of core allocations of the replica economy shrinks to the set of competitive allocations. Florenzano (1989) defines the fuzzy core as the set of allocations which cannot be blocked by any coalition with an arbitrary rate of participation and then shows the asymptotic limit of cores of replica economics coincides with the fuzzy core. In this note, we provide an elementary proof of the non-emptiness of the fuzzy core for an exchange economy. Unlike the classical Debreu-Scarf limit theorem and its numerous extensions our result does not require any asymptotic intersection -or limit- of the set of core allocations of replica economies. |
| Keywords: | Fuzzy core, Payoff-dependent balancedness, Exchange economies. |
| JEL: | D51 C71 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp531&r=gth |
| By: | Giorgio Fagiolo |
| Abstract: | We study equilibrium selection in coordination games played by a population whose size increases over time. In each time period, a new player enters the economy, observes current strategy shares and irreversibly chooses a strategy on the basis of expected payoffs. We employ a simple Polya-Urn scheme to discuss the efficiency of long-run equilibria under alternative individual decision rules (e.g. best-reply, logit, etc.). We show that the system delivers a predictable outcome only when agents employ either a linear or a logit probability rule. If agents employ deterministic best-reply rules, Pareto-efficient coordination can occur, but the actual outcome depends on initial conditions and chance. In all other cases, coexistence of strategies characterizes equilibrium configurations. |
| Keywords: | Coordination Games, Equilibrium Selection, Pareto-Efficient vs. Risk- Dominant Equilibrium, Polya-Urn Schemes. |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2005/05&r=gth |
| By: | Roger Lagunoff (Georgetown University) |
| Abstract: | This paper studies dynamic, endogenous institutional change. We introduce the class of dynamic political games (DPGs), dynamic games in which future political aggregation rules are decided under current ones, and the resulting institutional choices do not affect payoffs or technology directly. A companion paper (Lagunoff (2005b)) establishes existence of Markov Perfect equilibria of dynamic political games. The present paper examines issues of stability and reform when such equilibria exist. Which environments tend toward institutional stability? Which tend toward reform? We show that when political rules are dynamically consistent and private sector decisions areinessential,reform never occurs: all political rules are stable. Roughly,private sector decisions are inessential if any feasible ``social' continuation payoff can achieved by public sector decisions alone. More generally, we identify sufficient conditions for stability and reform in terms of recursive self selection and recursive self denial,incentive compatibility concepts that treat the rules themselves as ``players' who can strategically delegate future policy-making authority to different institutional types. These ideas are illustrated in an example of dynamic public goods provision. |
| Keywords: | Recursive, dynamic political games, institutional reform, stability, dynamically consistent rules, inessential, recursive self selection. |
| JEL: | C73 D72 D74 |
| Date: | 2005–05–12 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpga:0505006&r=gth |
| By: | Sami Dakhlia (University of Alabama); Frank H. Page Jr. (University of Alabama) |
| Abstract: | We model the agenda formation process as a network. In an agenda network, nodes represent agendas while arcs represent coalition preferences over agendas and coalitional moves from one agenda to another. We show that all agenda networks have agenda nodes which are farsightedly consistent. These nodes represent agendas which are likely to emerge and persist if agents behave farsightedly in forming agendas. We demonstrate the usefulness of our approach by computing the farsightedly consistent agendas for three examples of agenda networks. |
| Keywords: | directed networks, farsighted stability |
| JEL: | D7 |
| Date: | 2005–05–12 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwppe:0505003&r=gth |
| By: | Flavio Menezes (Australian National University); John Quiggin (Department of Economics, University of Queensland) |
| Abstract: | We introduce the notion of an outcome space, in which strategic interactions are embedded. This allows us to investigate the idea that one strategic interaction might be an expanded version of another interaction. We then characterize the Nash equilibria arising in such extensions and demonstrate a folk-type theorem stating that any individually rational element of the outcome space is a Nash equilibrium. |
| Keywords: | game theory |
| JEL: | C71 |
| Date: | 2004–07 |
| URL: | http://d.repec.org/n?u=RePEc:rsm:riskun:r04_7&r=gth |
| By: | Myrna Wooders (Department of Economics, Vanderbilt University); Edward Cartwright (Department of Economics, Keynes College, University of Kent); Reinhard Selten (Department of Economics, University of Bonn) |
| Abstract: | In the literature of psychology and economics it is frequently observed that individuals tend to conform in their behavior to the behavior of similar individuals. A fundamental question is whether the outcome of such behavior can be consistent with self-interest. We propose that this consistency requires the existence of a Nash or approximate Nash equilibrium that induces a partition of the player set into relatively few societies, each consisting of similar individuals playing the same or similar strategies. In this paper we introduce a notion of a society and characterize a family of games admitting the existence of such an equilibrium. We also introduce the concept of 'crowding types' into our description of players and distinguish between the crowding type of a player -- those characteristics of a player that have direct effects on others -- and his tastes, taken to directly affect only that player. With the assumptions of 'within crowding type anonymity' and 'linearity of taste-types' we show that the number of groups can be uniformly bounded. |
| Keywords: | Behavioral conformity, noncooperative games, pregames, Nash equilibrium, purification, social norms, behavioral norms |
| JEL: | C72 Z13 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0513&r=gth |
| By: | John P. Conley (Department of Economics, Vanderbilt University); Myrna Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | We consider the classic puzzle of why people turn out for elections in substantial numbers even though formal analysis strongly suggests that rational agents would not vote. If one assumes that voters do not make systematic mistakes, the most plausible explanation seems to be that agents receive a warm glow from the act of voting itself. However, this begs the question of why agents feel a warm glow from participating in the electoral process in the first place. We approach this question from an memetic standpoint. More specifically, we consider a model in which social norms, ideas, values, or more generally, "memes" influence the behavior of groups of agents, and in turn, induce a kind of competition between value systems. We show for a range of situations that groups with a more public-spirited social norm have an advantage over groups that are not as public-spirited. We also explore conditions under which the altruistic behavior resulting from public-spiritedness is disadvantageous. The details depend on the costs of voting, the extent to which different types of citizens agree or disagree over the benefits of various public policies, and the relative proportions of various preference types in the population. We conclude that memetic evolution over social norms may be a force that causes individuals to internalize the benefits that their actions confer on others. |
| Keywords: | Memetics, evolution, voting, warm glow, civic duty, free riding, public choice, public goods |
| JEL: | C7 D7 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0514&r=gth |
| By: | Ronald M. Harstad (Department of Economics, University of Missouri-Columbia) |
| Abstract: | Potential bidders respond to a seller's choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur a participation cost (and observe a private signal), or forego competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior for any common-value auction. Characterization of optimal auctions is otherwise contentless, in that any auction that sells without reserve is within the setting of one continuous parameter of an optimal auction; seller's surplus-extracting tools are now substitutes, not complements. Revenue comparisons from the exogenous-bidders literature are upheld in a half-space of parameters, overturned in a half-space. Many econometric studies of auction markets are seen to be flawed in their identifcation of the number of bidders. |
| Keywords: | optimal auctions, endegenous bidder participation, affiliated-values, common-value auctions, surplus-extracting devices |
| JEL: | D44 D82 C72 |
| Date: | 2005–05–10 |
| URL: | http://d.repec.org/n?u=RePEc:umc:wpaper:0504&r=gth |
| By: | Manjira Datta (W. P. Carey School of Business Department of Economics); Tito Cordella (International Monetary Fund) |
| Abstract: | In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an ineffciency which does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., moving towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., moving away from the Walrasian amount). |
| JEL: | C72 C73 D43 D90 |
| URL: | http://d.repec.org/n?u=RePEc:asu:wpaper:2132843&r=gth |