Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound by reducing it to Kozen’s metric coinduction. We characterize all subgame perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the payoffs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics

Intelligent escalation and the principle of relativity

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 cognitive psychology the difference between intelligence (algorithmic mind) and rationality (algorithmic and reflective mind) in decision processes. It also shows that depending on the point of view (inside or outside) the rationality of the agent may change which is proposed to be called the principle of relativity.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228

Infinite subgame perfect equilibrium in the Hausdorff difference hierarchy

Subgame perfect equilibria are specific Nash equilibria in perfect information games in extensive form. They are important because they relate to the rationality of the players. They always exist in infinite games with continuous real-valued payoffs, but may fail to exist even in simple games with slightly discontinuous payoffs. This article considers only games whose outcome functions are measurable in the Hausdorff difference hierarchy of the open sets (\textit{i.e.} $\Delta^0_2$ when in the Baire space), and it characterizes the families of linear preferences such that every game using these preferences has a subgame perfect equilibrium: the preferences without infinite ascending chains (of course), and such that for all players $a$ and $b$ and outcomes $x,y,z$ we have $\neg(z <_a y <_a x \,\wedge\, x <_b z <_b y)$. Moreover at each node of the game, the equilibrium constructed for the proof is Pareto-optimal among all the outcomes occurring in the subgame. Additional results for non-linear preferences are presented.Comment: The alternative definition of the difference hierarchy has changed slightl

Bridging Disciplinary Gaps in Studies of Human-Environment Relations: A Modelling Framework

Modern human-environment relations are problematic and difficult to analyse in terms of nature and culture. Many authors suggest to abandon and overcome the nature-culture dichotomy in order to reorganise the academic division of labour, not only on environmental questions. Anthropologist Philippe Descola, for example, surveyed the empirical evidence of patterns in humanenvironmental relations, suggesting four abstract cosmologies. Here, we propose a translation into a modelling terminology, which is compatible with the formalisation of programmes in computer science. The generalised framework contains four ideal types of modelling paradigms. It can be tested on various other classification schemes in a number of disciplines. In each application, the categories of classification can be translated and then the patterns of the four logic types can be compared with the phenomenology of each case. Implications for interdisciplinary cooperation between science and the humanities are sketched for some environmental issues. This work demonstrates how tools from computer science can help, metaphorically, conceptually and technically, to organise interdisciplinary exchanges between science and the humanities. The categorical approach of applying the “divide and conquer” technique to different disciplinary models serves as a yardstick for comparing the implicit logic and modelling assumptions across examples whose phenomenological contents appear as unrelated. It gives useful hints how a dilemma of choosing between rigorous or relevant models can be resolved (e.g., in environmental science) and how the nature-culture dichotomy might be replaced by a general and flexible framework of a few model types

Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics.ISSN:0960-1295ISSN:1469-807

Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics

Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame-perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound. We characterize all subgame-perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the pay-offs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics