Although the definition of what empathetic preferences exactly are is still evolving, there is a general consensus in the psychology, science and engineering communities that the evolution toward players' behaviors in interactive decision-making problems will be accompanied by the exploitation of their empathy, sympathy, compassion, antipathy, spitefulness, selfishness, altruism, and self-abnegating states in the payoffs. In this article, we study one-shot bimatrix games from a psychological game theory viewpoint. A new empathetic payoff model is calculated to fit empirical observations and both pure and mixed equilibria are investigated. For a realized empathy structure, the bimatrix game is categorized among four generic class of games. Number of interesting results are derived. A notable level of involvement can be observed in the empathetic one-shot game compared the non-empathetic one and this holds even for games with dominated strategies. Partial altruism can help in breaking symmetry, in reducing payoff-inequality and in selecting social welfare and more efficient outcomes. By contrast, partial spite and self-abnegating may worsen payoff equity. Empathetic evolutionary game dynamics are introduced to capture the resulting empathetic evolutionarily stable strategies under wide range of revision protocols including Brown-von Neumann-Nash, Smith, imitation, replicator, and hybrid dynamics. Finally, mutual support and Berge solution are investigated and their connection with empathetic preferences are established. We show that pure altruism is logically inconsistent, only by balancing it with some partial selfishness does it create a consistent psychology.
In the 1880s, [pages 102-104] edge introduced the idea of other-regarding payoff transformations as follows: player @math maximizes the payoff function @math where @math Here @math and @math represent relative weights that @math assigns to @math (own) and @math (to the other player's) non-empathetic payoff, respectively. The work in @cite_9 proposed an interesting model of partial altruism as an explanation for the results of public good contribution games, where a player's utility is a linear function of both the player's own monetary payoff and the other players' payoffs. The work in @cite_4 @cite_2 proposed a model that uses both spite and altruism, where the adjusted utility of a player reflects the player's own utility and his regard for other players. A model of fairness is proposed in @cite_10 where in addition to purely selfish players, there are players who dislike inequitable outcomes.
@cite_10 @cite_9 @cite_4 @cite_2
2099758346 1995275762 2964436851 2161061197
We examine a simple theory of altruism in which players' payoffs are linear in their own monetary income and their opponents. The weight on the opponent's income is private information and varies in the population, depending, moreover, on what the opponent's coefficient is believed to be. Using results of ultimatum experiments and the final round of a centipede experiment, we are able to pin down relatively accurately what the distribution of altruism (and spite) in the population is. This distribution is then used with a reasonable degree of success to explain the results of the earlier rounds of centipede and the results of some public goods contribution games. In addition, we show that in a market game where the theory of selfish players does quite well, the theory of altruism makes exactly the same predictions as the theory of selfish players. (Copyright: Elsevier) We consider the problem of maximizing welfare when allocating m items to n players with subadditive utility functions. Our main result is a way of rounding any fractional solution to a linear programming relaxation to this problem so as to give a feasible solution of welfare at least half that of the value of the fractional solution. This approximation ratio of 1 2 improves over an Ω(1 log m) ratio of Dobzinski, Nisan and Schapira [STOC 2005]. We also show an approximation ratio of 1 - 1 e when utility functions are fractionally subadditive. A result similar to this last result was previously obtained by Dobzinski and Schapira [Soda 2006], but via a different rounding technique that requires the use of a so called "XOS oracle".The randomized rounding techniques that we use are oblivious in the sense that they only use the primal solution to the linear program relaxation, but have no access to the actual utility functions of the players. This allows us to suggest new incentive compatible mechanisms for combinatorial auctions, extending previous work of Lavi and Swamy [FOCS 2005]. We consider the problem of fairly dividing a collection of indivisible goods among a set of players. Much of the existing literature on fair division focuses on notions of individual fairness. For instance, envy-freeness requires that no player prefer the set of goods allocated to another player to her own allocation. We observe that an algorithm satisfying such individual fairness notions can still treat groups of players unfairly, with one group desiring the goods allocated to another. Our main contribution is a notion of group fairness, which implies most existing notions of individual fairness. Group fairness (like individual fairness) cannot be satisfied exactly with indivisible goods. Thus, we introduce two “up to one good” style relaxations. We show that, somewhat surprisingly, certain local optima of the Nash welfare function satisfy both relaxations and can be computed in pseudo-polynomial time by local search. Our experiments reveal faster computation and stronger fairness guarantees in practice. We consider the problem of designing (perhaps massively distributed) collectives of computational processes to maximize a provided "world utility" function. We consider this problem when the behavior of each process in the collective can be cast as striving to maximize its own payoff utility function. For such cases the central design issue is how to initialize update those payoff utility functions of the individual processes so as to induce behavior of the entire collective having good values of the world utility. Traditional "team game" approaches to this problem simply assign to each process the world utility as its payoff utility function. In previous work we used the "Collective Intelligence" (COIN) framework to derive a better choice of payoff utility functions, one that results in world utility performance up to orders of magnitude superior to that ensuing from the use of the team game utility. In this paper, we extend these results using a novel mathematical framework. Under that new framework we review the derivation of the general class of payoff utility functions that both (i) are easy for the individual processes to try to maximize, and (ii) have the property that if good values of them are achieved, then we are assured a high value of world utility. These are the "Aristocrat Utility" and a new variant of the "Wonderful Life Utility" that was introduced in the previous COIN work. We demonstrate experimentally that using these new utility functions can result in significantly improved performance over that of previously investigated COIN payoff utilities, over and above those previous utilities' superiority to the conventional team game utility. These results also illustrate the substantial superiority of these payoff functions to perhaps the most natural version of the economics technique of "endogenizing externalities."