A constructive approach to sequential Nash equilibria

“Backward” coinduction, Nash equilibrium and the rationality of escalation

“…Other applications are on representation of real numbers by infinite sequences [3,18] and implementation of streams (infinite lists) in electronic circuits [11]. An ancestor of our description of infinite games and infinite strategy profiles is the constructive description of finite games, finite strategy profiles, and equilibria by Vestergaard [32]. Lescanne [20] introduces the framework of infinite games with more detail.…”

“…Another approach which Osborne [25] attributes to Rubinstein uses histories. A third approach proposed by Vestergaard [32] which fits well with inductive reasoning is to give an inductive definition of games. To handle infinite games we propose a coinductive definition.…”

“…Notice that in such games, it can be the case that the same agent a has the turn twice in a row, like in the game (gNode a (gNode a g 1 g 2 ) g 3 ). This definition, already adopted by Vestergaard [32], is less restrictive and makes definitions easier since the formalism is more general. Moreover, it contains the case when players play in alternation, but also games where positions do not allow some players to act, making one or a subgroup of players to play in a row, because the others cannot.…”

Rewriting Game Theory as a Foundation for State-Based Models of Gene Regulation

“…At that point, also a 1 can benefit from changing his choice and, in fact, the only Nash equilibrium in the game is a 1 (a 2 ) going left (right). Nash equilibria can be guaranteed to exist for all sequential games, a result known as Kuhn's Theorem [7,20].…”

Towards Formal Foundations for Game Theory

“…Gammie has formalized some results in social choice theory, as well as stable matching [4,5]. Kuhn's theorem has been formalized by Vestergaard [21] and generalized by Le Roux [17]. The same author later worked on a formalization of Nash equilibria for two player games [18].…”