Title: Empathy in Bimatrix Games,
Abstract: 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.