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on Game Theory |
| By: | Nunez, Marina; Solymosi, Tamás |
| Abstract: | We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We first investigate the general relationship between these allocations and obtain two hierarchies on the class of balanced games. Secondly, we focus on assignment games and sharpen some of these general relationship. Our main result is the coincidence of the sets of lemarals (vectors of lexicographic maxima over the set of dual coalitionally rational payoff vectors), lemacols (vectors of lexicographic maxima over the core) and extreme core points. As byproducts, we show that, similarly to the core and the coalitionally rational payoff set, also the dual coalitionally rational payoff set of an assignment game is determined by the individual and mixed-pair coalitions, and present an efficient and elementary way to compute these basic dual coalitional values. This provides a way to compute the Alexia value (the average of all lemacols) with no need to obtain the whole coalitional function of the dual assignment game. |
| Keywords: | assignment game, Alexia value |
| Date: | 2014–10–08 |
| URL: | http://d.repec.org/n?u=RePEc:cvh:coecwp:2014/15&r=gth |
| By: | Jan Zapal |
| Abstract: | The paper proves, by construction, the existence of Markovian equilibria in a model of dynamic spatial legislative bargaining. Players bargain over policies in an infinite horizon. In each period, a majority vote takes place between the proposal of a randomly selected player and the status-quo, the policy last enacted. This determines the policy outcome that carries over as the status-quo in the following period; the status-quo is endogenous. Proposer recognition probabilities are constant and discount factors are homogeneous. The construction relies on simple strategies determined by strategic bliss points computed by the algorithm we provide. A strategic bliss point is the policy maximizing the dynamic utility of a player with ample bargaining power. Relative to a bliss point, the static utility ideal, a strategic bliss point is a moderate policy. Moderation is strategic and germane to the dynamic environment; players moderate in order to constrain the future proposals of opponents. Moderation is a strategic substitute; when a player's opponents do moderate, she does not, and when they do not moderate, she does. We prove that the simple strategies induced by the strategic bliss points computed by the algorithm deliver a Stationary Markov Perfect equilibrium. Thus we prove its existence in a large class of symmetric games with more than three players and (possibly with slight adjustment) in any three-player game. Because the algorithm constructs all equilibria in simple strategies, we provide their general characterization, and we show their generic uniqueness. Finally, we analyse how the degree of moderation changes with changes in the model parameters, and we discuss the dynamics of the equilibrium policies. |
| Keywords: | dynamic decision-making; endogenous status-quo; spatial bargaining; legislative bargaining; |
| JEL: | C73 C78 D74 D78 |
| Date: | 2014–08 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp515&r=gth |
| By: | Frank Riedel (Center for Mathematical Economics, Bielefeld University); Jan-Henrik Steg (Center for Mathematical Economics, Bielefeld University) |
| Abstract: | We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies - in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications. |
| Keywords: | timing games, stochastic games, mixed strategies, subgame-perfect equilibrium in continuous time, optimal stopping |
| JEL: | C61 C73 D21 L12 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:524&r=gth |
| By: | Takao Asano (Okayama University); Takuma Kunieda (City University of Hong Kong); Akihisa Shibata (Institute of Economic Research, Kyoto University) |
| Abstract: | Using a simple framework of Cooper and John (1988) and Cooper (1999), this paper derives the conditions under which overconfidence and underconfidence of agents lead to Pareto improvement. We show that an agent’s overconfidence in a game exhibiting strategic complementarity and positive spillovers and an agent’s underconfidence in a game exhibiting strategic complementarity and negative spillovers can lead to Pareto improvement. |
| Keywords: | overconfidence, underconfidence, strategic complementarity, strategic substitutability, positive spillover, negative spillover |
| JEL: | D62 C72 |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:903&r=gth |
| By: | ANDERSSON, Tommy; EHLERS, Lars; LARS-GUNNAR, Svensson |
| Abstract: | This paper explores situations where tenants in public houses, in a specific neighborhood, are given the legislated right to buy the houses they live in or can choose to remain in their houses and pay the regulated rent. This type of legislation has been passed in many European countries in the last 30-35 years (the U.K. Housing Act 1980 is a leading example). The main objective with this type of legislation is to transfer the ownership of the houses from the public authority to the tenants. To achieve this goal, selling prices of the public houses are typically heavily subsidized. The legislating body then faces a trade-off between achieving the goals of the legislation and allocating the houses efficiently. This paper investigates this specific trade-off and identifies an allocation rule that is individually rational, equilibrium selecting, and group non-manipulable in a restricted preference domain that contains “almost all” preference profiles. In this restricted domain, the identified rule is the equilibrium selecting rule that transfers the maximum number of ownerships from the public authority to the tenants. This rule is preferred to the current U.K. system by both the existing tenants and the public authority. Finally, a dynamic process for finding the outcome of the identified rule, in a finite number of steps, is provided. |
| Keywords: | Public housing; existing tenants; equilibrium; minimum equilibrium prices; maximum trade; group non-manipulability; dynamic price process |
| JEL: | C71 C78 D71 D78 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2014-05&r=gth |
| By: | Erhan Bayraktar; Zhou Zhou |
| Abstract: | On a filtered probability space $(\Omega,\mathcal{F},P,\mathbb{F}=(\mathcal{F}_t)_{0\leq t\leq T})$, we consider stopper-stopper games $\bar C:=\inf_{\Rho}\sup_{\tau\in\T}\E[U(\Rho(\tau),\tau)]$ and $\underline C:=\sup_{\Tau}\inf_{\rho\in\T}\E[U(\Rho(\tau),\tau)]$ in continuous time, where $U(s,t)$ is $\mathcal{F}_{s\vee t}$-measurable (this is the new feature of our stopping game), $\T$ is the set of stopping times, and $\Rho,\Tau:\T\mapsto\T$ satisfy certain non-anticipativity conditions. We show that $\bar C=\underline C$, by converting these problems into a corresponding Dynkin game. |
| Date: | 2014–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1409.6773&r=gth |
| By: | G. Gaballo |
| Abstract: | This paper explores convergence in higher-order beliefs - otherwise called eductive stability - when coordination is sequential, that is, when each agent of a given type fixes his own actions after observing the ones of earlier types in a given order. The presence of sequential types enhances expectational coordination in case of strategic substitutability, but not in case of strategic complementarity. In particular eductive stability can be obtained for any degree of substitutability, provided the number of sequential types is large enough. Therefore, sequential coordination opens up to the possibility that eductive convergence occurs at the same conditions of adaptive convergence, in accordance to the E-stability principle. |
| Keywords: | eductive learning, rational expectation equilibria, rationalizable set, learning in macroeconomics, coordination games. |
| JEL: | D41 E30 B41 |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:bfr:banfra:509&r=gth |
| By: | NEGRI, Margherita; SPRUMONT, Yves |
| Abstract: | A measure of association is row-size invariant if it is unaffected by the multiplication of all entries in a row of a cross-classification table by a same positive number. It is class-size invariant if it is unaffected by the multiplication of all entries in a class (i.e., a row or a column). We prove that every class-size invariant measure of association as-signs to each m x n cross-classification table a number which depends only on the cross-product ratios of its 2 x 2 subtables. We propose a monotonicity axiom requiring that the degree of association should increase after shifting mass from cells of a table where this mass is below its expected value to cells where it is above-provided that total mass in each class remains constant. We prove that no continuous row-size invariant measure of association is monotonic if m ≥ 4. Keywords: association, contingency tables, margin-free measures, size invariance, monotonicity, transfer principle. |
| Date: | 2014 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montde:2014-06&r=gth |
| By: | Selman Erol (Department of Economics, University of Pennsylvania); Rakesh Vohra (Department of Economics and Department of Electrical & Systems Engineering, University of Pennsylvania) |
| Abstract: | This paper introduces a model of endogenous network formation and systemic risk. In it, agents form networks that efficiently trade-off the possibility of systemic risk with the benefits of trade. Second, fundamentally ‘safer’ economies generate higher interconnectedness, which in turn leads to higher systemic risk. Third, the structure of the network formed depends on whether the shocks to the system are believed to be correlated or independent of each other. In particular, when shocks are perfectly correlated, the network formed is a complete graph, i.e., a link between every pair of agents. This underlines the importance of specifying the shock structure before investigating a given network because a given network and shock structure could be incompatible. |
| Keywords: | Network Formation, Systemic Risk, Contagion, Rationalizability, Core |
| JEL: | D85 G01 |
| Date: | 2014–08–24 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:14-029&r=gth |