Related papers: Extensive Infinite Games and Escalation, an exerci…
Escalation is the fact that in a game (for instance an auction), the agents play forever. It is not necessary to consider complex examples to establish its rationality. In particular, the $0,1$-game is an extremely simple infinite game in…
Escalation is the fact that in a game (for instance in an auction), the agents play forever. The $0,1$-game is an extremely simple infinite game with intelligent agents in which escalation arises. It shows at the light of research on…
The aim of this of this paper is to study infinite games and to prove formally some properties in this framework. As a consequence we show that the behavior (the madness) of people which leads to speculative crashes or escalation can be…
Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its…
Escalation is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its…
As we show using the notion of equilibrium in the theory of infinite sequential games, bubbles and escalations are rational for economic and environmental agents, who believe in an infinite world. This goes against a vision of a self…
Extensive-form games constitute the standard representation scheme for games with a temporal component. But do all extensive-form games correspond to protocols that we can implement in the real world? We often rule out games with imperfect…
Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…
In order to better understand reasoning involved in analyzing infinite games in extensive form, we performed experiments in the proof assistant Coq that are reported here.
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
As we show by using notions of equilibrium in infinite sequential games, crashes or financial escalations are rational for economic or environmental agents, who have a vision of an infinite world. This contradicts a picture of a…
Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players…
A sequential decision-making agent balances between exploring to gain new knowledge about an environment and exploiting current knowledge to maximize immediate reward. For environments studied in the traditional literature, optimal…
We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his…
Extensive games are tools largely used in economics to describe decision processes ofa community of agents. In this paper we propose a formal presentation based on theproof assistant COQ which focuses mostly on infinite extensive games and…
Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a…
Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies.…