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  • 1. Alger, I.
    et al.
    Weibull, Jörgen W.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Stockholm School of Economics, Sweden.
    Strategic behavior of moralists and altruists2017In: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 8, no 3, article id 38Article in journal (Refereed)
    Abstract [en]

    Does altruism and morality lead to socially better outcomes in strategic interactions than selfishness? We shed some light on this complex and non-trivial issue by examining a few canonical strategic interactions played by egoists, altruists and moralists. By altruists, we mean people who do not only care about their own material payoffs but also about those to others, and, by a moralist, we mean someone who cares about own material payoff and also about what would be his or her material payoff if others were to act like himself or herself. It turns out that both altruism and morality may improve or worsen equilibrium outcomes, depending on the nature of the game. Not surprisingly, both altruism and morality improve the outcomes in standard public goods games. In infinitely repeated games, however, both altruism and morality may diminish the prospects of cooperation, and to different degrees. In coordination games, morality can eliminate socially inefficient equilibria while altruism cannot.

  • 2. Asheim, G. B.
    et al.
    Voorneveld, M.
    Weibull, J. W.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Epistemically robust strategy subsets2016In: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 7, no 4, article id 37Article in journal (Refereed)
    Abstract [en]

    We define a concept of epistemic robustness in the context of an epistemic model of a finite normal-form game where a player type corresponds to a belief over the profiles of opponent strategies and types. A Cartesian product X of pure-strategy subsets is epistemically robust if there is a Cartesian product Y of player type subsets with X as the associated set of best reply profiles such that the set Yi contains all player types that believe with sufficient probability that the others are of types in Y-i and play best replies. This robustness concept provides epistemic foundations for set-valued generalizations of strict Nash equilibrium, applicable also to games without strict Nash equilibria. We relate our concept to closedness under rational behavior and thus to strategic stability and to the best reply property and thus to rationalizability.

  • 3.
    Aurell, Alexander
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Mean-Field Type Games between Two Players Driven by Backward Stochastic Differential Equations2018In: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 9, no 5Article in journal (Refereed)
    Abstract [en]

    In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum, non-cooperating, differential games where the players’ state dynamics solve backward stochastic differential equations (BSDE) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of playercosts, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

  • 4.
    Choutri, Salah eddine
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Hamidou, Tembine
    A Stochastic Maximum Principle for Markov Chains of Mean-Field Type2018In: Games, ISSN 2073-4336, E-ISSN 2073-4336, Vol. 9, no 4, article id 84Article in journal (Refereed)
    Abstract [en]

    We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications. 

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