English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Game theory is widely used as a behavioral model for strategic interactionsin biology and social science. It is common practice to assume that playersquickly converge to an equilibrium, e.g. a Nash equilibrium. This can bestudied in terms of best reply dynamics, in which each player myopically usesthe best response to her opponent's last move. Existing research shows thatconvergence can be problematic when there are best reply cycles. Here wecalculate how typical this is by studying the space of all possible two-playernormal form games and counting the frequency of best reply cycles. The two keyparameters are the number of moves, which defines how complicated the game is,and the anti-correlation of the payoffs, which determines how competitive itis. We find that as games get more complicated and more competitive, best replycycles become dominant. The existence of best reply cycles predictsnon-convergence of six different learning algorithms that have support fromhuman experiments. Our results imply that for complicated and competitive gamesequilibrium is typically an unrealistic assumption. Alternatively, if for somereason "real" games are special and do not possess cycles, we raise theinteresting question of why this should be so.

Best reply structure and equilibrium convergence in generic games