Chess endgame news

This note defines what it means by the 'chess endgame' and looks at the frequency of sub-n-man and 'FinalGen' positions in games and studies and in the FIDE 2013 World Cup. It includes the exposition of the DTM-minimaxing line from one of the three DTM-deepest known (KQPKRBN) positions. It refines the definitions of 'longest game' and 'bionic game'. The games of the FIDE 2013 World Cup and the longest known decisive game are available here.

Bargaining over strategies of non-cooperative games

We propose a bargaining process supergame over the strategies to play in a non-cooperative game. The agreement reached by players at the end of the bargaining process is the strategy profile that they will play in the original non-cooperative game. We analyze the subgame perfect equilibria of this supergame, and its implications on the original game. We discuss existence, uniqueness, and efficiency of the agreement reachable through this bargaining process. We illustrate the consequences of applying such a process to several common two-player non-cooperative games: the Prisoner’s Dilemma, the Hawk-Dove Game, the Trust Game, and the Ultimatum Game. In each of them, the proposed bargaining process gives rise to Pareto-efficient agreements that are typically different from the Nash equilibrium of the original games.