What modern game theorists describe as 'fictitious play' is not the learning process George W. Brown defined in his 1951 paper. His original version differs in a subtle detail, namely the order of belief updating. In this note we revive Brown's original fictitious play process and demonstrate...

Fictitious play is the classical myopic learning process, and games with strategic complementarities are an important class of games including many economic applications. Knowledge about convergence properties of fictitious play in this class of games is scarce, however. Beyond dominance...

It is known that every continuous time fictitious play process approaches equilibrium in every nondegenerate 2x2 and 2x3 game, and it has been conjectured that convergence to equilibrium holds generally for 2xn games. We give a simple geometric proof of this.

This paper studies fictitious play in networks of noncooperative two-player games. We show that continuous-time fictitious play converges to Nash equilibrium provided that the overall game is zero-sum. Moreover, the rate of convergence is 1/T , regardless of the size of the network. In contrast,...

This paper studies fictitious play in networks of noncooperative two-person games. We show that continuous-time fictitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1/T, regardless of the size of the network. In...

This paper studies fictitious play in networks of noncooperative two-person games. We show that continuous-time fictitious play converges to the set of Nash equilibria if the overall n-person game is zero-sum. Moreover, the rate of convergence is 1/T, regardless of the size of the network. In...

This paper studies fictitious play in networks of noncooperative two-player games. We show that continuous-time fictitious play converges to Nash equilibrium provided that the overall game is zero-sum. Moreover, the rate of convergence is 1/T , regardless of the size of the network. In contrast,...

This paper studies the evolution of peoples' models of how other people think - their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found...

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The 'TASP' (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We...

We study the Fictitious Play process with bounded and unbounded recall in pure coordination games for which failing to coordinate yields a payoff of zero for both players. It is shown that every Fictitious Play player with bounded recall may fail to coordinate against his own type. On the other...