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Robert Aumann ’ s and Thomas Schelling ’ s Contributions to Game Theory : Analyses of Conflict and Cooperation

1. Introduction Wars and other conflicts are among the main sources of human misery. A minimum of cooperation is a prerequisite for a prosperous society. Life in an anarchic " state of nature " with its struggle of every man against every man is, in Thomas Hobbes' (1651) famous phrase, " solitary, poor, nasty, brutish, and short ". Social scientists have long attempted to understand the fundamental causes of conflict and cooperation. The advent of game theory in the middle of the twentieth century led to major new insights and enabled researchers to analyze the subject with mathematical rigor. The foundations of game theory were laid out in the classic book added solution concepts and insights that substantially enhanced the usefulness and predictive power of non-cooperative game theory. The most central solution concept is that of Nash equilibrium. A strategy combination (one strategy for each player) constitutes a Nash equilibrium if each player's strategy is optimal against the other players' strategies.