The geometry of inductive reasoning in games

This paper contributes to the recent focus on dynamics in noncooperative games when players use inductive learning. The most well-known inductive learning rule, Brown's fictitious play, is known to converge for $2 \times 2$ games, yet many examples exist where fictitious play reasoning fails to converge to a Nash equilibrium. Building on ideas from chaotic dynamics, this paper develops a geometric conceptualization of instability in games, allowing for a reinterpretation of existing results and suggesting avenues for new results.