Fix finite pure strategy sets <formula format="inline"> <simplemath>_S1 <roman>,</roman>… <roman>,</roman>_Sn </simplemath> </formula>, and let <formula format="inline"> <simplemath>S&equals;_S1×&ctdot;×_Sn </simplemath> </formula>. In our model of a random game the agents' payoffs are statistically independent, with each agent's payoff uniformly distributed on the unit sphere in <openface>R</openface>-super-S. For given nonempty <formula format="inline"> <simplemath>_T1⊂_S1 <roman>,</roman>… <roman>,</roman>_Tn⊂_Sn </simplemath> </formula> we give a...

Consider nonempty finite pure strategy sets S[subscript 1], . . . , S[subscript n], let S = S[subscript 1] times . . . times S[subscript n], let Omega be a finite space of "outcomes," let Delta(Omega) be the set of probability distributions on Omega, and let theta: S approaches Delta(Omega) be a...

An allocation for an exchange economy with smooth preferences is shown to be Walrasian if there is a set of net trades that is closed under addition, contains the negations of net trades that would improve any agent's final bundle, and is such that each agent's final bundle is weakly preferred...