3,181 research outputs found

    Incentive Stackelberg Mean-payoff Games

    Get PDF
    We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader equilibria, there is a distinguished player called the leader who can assign strategies to all other players, referred to as her followers. A strategy profile is a leader strategy profile if no player, except for the leader, can improve his payoff by changing his strategy unilaterally, and a leader equilibrium is a leader strategy profile with a maximal return for the leader. In the proposed case of incentive equilibria, the leader can additionally influence the behaviour of her followers by transferring parts of her payoff to her followers. The ability to incentivise her followers provides the leader with more freedom in selecting strategy profiles, and we show that this can indeed improve the payoff for the leader in such games. The key fundamental result of the paper is the existence of incentive equilibria in mean-payoff games. We further show that the decision problem related to constructing incentive equilibria is NP-complete. On a positive note, we show that, when the number of players is fixed, the complexity of the problem falls in the same class as two-player mean-payoff games. We also present an implementation of the proposed algorithms, and discuss experimental results that demonstrate the feasibility of the analysis of medium sized games.Comment: 15 pages, references, appendix, 5 figure

    Putting Free-Riding to Work: A Partnership Solution to the Common-Property Problem

    Get PDF
    The common-property problem results in excessive mining, hunting, and extraction of oil and water. The same phenomenon is also responsible for excessive investment in R&D and excessive outlays in rent-seeking contests. We propose a "Partnership Solution" to eliminate or at least mitigate these excesses. Each of N players joins a partnership in the first stage and chooses his effort in the second stage. Under the rules of a partnership, each member must pay his own cost of effort but receives an equal share of the partnership's revenue. The incentive to free-ride created by such partnerships turns out to be beneficial since it naturally offsets the excessive effort inherent in such problems. In our two-stage game, this institutional arrangement can, under specified circumstances, induce the social optimum in a subgame-perfect equilibrium: no one has a unilateral incentive (1) to switch to another partnership (or create a new partnership) in the first stage or (2) to deviate from socially optimal actions in the second stage. The game may have other subgame-perfect equilibria, but the one associated with the ``Partnership Solution'' is strictly preferred by every player. We also propose a modification of the first stage which generates a unique subgame-perfect equilibrium. Antitrust authorities should recognize that partnerships can have a less benign use. By organizing as competing partnerships, an industry can reduce the ``excessive'' output of Cournot oligopoly to the monopoly level. Since no partner has any incentive to overproduce in the current period, there is no need to deter cheating with threats of future punishments.partnerships;common property;tragedy of the commons;cartels

    Historical Legacies: A Model Linking Africa's Past to its Current Underdevelopment

    Get PDF
    Recent studies have found evidence linking Africa’s current underdevelopment to colonial rule and the slave trade. Given that these events ended long ago, why do they continue to matter today? I develop a model, exhibiting path dependence, that explains how these past events could have lasting impacts. The model has multiple equilibria: one equilibrium with secure property rights and a high level of production and others with insecure property rights and low levels of production. I show that external extraction, when severe enough, causes a society initially in the high production equilibrium to move to a low production equilibrium. Because of the stability of low production equilibria, the society remains trapped in this suboptimal equilibrium even after the period of external extraction ends. The model provides one explanation why Africa’s past events continue to matter today.

    Sufficient conditions for stable equilibria

    Get PDF
    A refinement of the set of Nash equilibria that satisfies two assumptions is shown to select a subset that is stable in the sense defined by Kohlberg and Mertens. One assumption requires that a selected set is invariant to adjoining redundant strategies and the other is a strong version of backward induction. Backward induction is interpreted as the requirement that each player's strategy is sequentially rational and conditionally admissible at every information set in an extensive-form game with perfect recall, implemented here by requiring that the equilibrium is quasi-perfect. The strong version requires 'truly' quasi-perfection in that each strategy perturbation refines the selection to a quasi-perfect equilibrium in the set. An exact characterization of stable sets is provided for two-player games.Game theory, equilibrium selection, stability

    A Re-Interpretation of Nash Equilibrium Based on the Notion of Social Institutions

    Get PDF
    We define social institutions as strategies in some repeated game. With this interpretation in mind, we consider the impact of introducing requirements on strategies which have been viewed as necessary properties for any social institution to endure. The properties we study are finite complexity, symmetry, global stability, and semi-perfection. We show that: (1) If a strategy satisfies these properties then players play a Nash equilibrium of the stage game in every period; (2) The set of finitely complex, symmetric, globally stable, semi-perfect equilibrium payoffs in the repeated game equals the set of Nash equilibria payoffs in the stage game; and (3) A strategy vector satisfies these properties in a Pareto optimal way if and only if players play some Pareto optimal Nash equilibrium of the stage game in every stage. These results provide a social institution interpretation of Nash equilibrium: individual behavior in enduring social institutions is described by Nash equilibria.Nash equilibrium, discounted repeated games, semi-perfect equilibrium, global stability, finite automata, social norms.

    Dynamics and Coalitions in Sequential Games

    Full text link
    We consider N-player non-zero sum games played on finite trees (i.e., sequential games), in which the players have the right to repeatedly update their respective strategies (for instance, to improve the outcome wrt to the current strategy profile). This generates a dynamics in the game which may eventually stabilise to a Nash Equilibrium (as with Kukushkin's lazy improvement), and we argue that it is interesting to study the conditions that guarantee such a dynamics to terminate. We build on the works of Le Roux and Pauly who have studied extensively one such dynamics, namely the Lazy Improvement Dynamics. We extend these works by first defining a turn-based dynamics, proving that it terminates on subgame perfect equilibria, and showing that several variants do not terminate. Second, we define a variant of Kukushkin's lazy improvement where the players may now form coalitions to change strategies. We show how properties of the players' preferences on the outcomes affect the termination of this dynamics, and we thereby characterise classes of games where it always terminates (in particular two-player games).Comment: In Proceedings GandALF 2017, arXiv:1709.0176

    The Simple Geometry of Perfect Information Games

    Get PDF
    Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.Perfect information, Subgame perfection, Equilibrium correspondence
    corecore