The use of multiplayer game theory in the modeling of biological populations

The use of game theory in modeling the natural world is widespread. However, this modeling mainly involves two player games only, or "playing the field" games where an individual plays against an entire (infinite) population. Game-theoretic models are common in economics as well, but in this case the use of multiplayer games has not been neglected. This article outlines where multiplayer games have been used in evolutionary modeling and the merits and limitations of these games. Finally, we discuss why there has been so little use of multiplayer games in the biological setting and what developments might be useful

Structure in the Value Function of Two-Player Zero-Sum Games of Incomplete Information

Zero-sum stochastic games provide a rich model for competitive decision making. However, under general forms of state uncertainty as considered in the Partially Observable Stochastic Game (POSG), such decision making problems are still not very well understood. This paper makes a contribution to the theory of zero-sum POSGs by characterizing structure in their value function. In particular, we introduce a new formulation of the value function for zs-POSGs as a function of the "plan-time sufficient statistics" (roughly speaking the information distribution in the POSG), which has the potential to enable generalization over such information distributions. We further delineate this generalization capability by proving a structural result on the shape of value function: it exhibits concavity and convexity with respect to appropriately chosen marginals of the statistic space. This result is a key pre-cursor for developing solution methods that may be able to exploit such structure. Finally, we show how these results allow us to reduce a zs-POSG to a "centralized" model with shared observations, thereby transferring results for the latter, narrower class, to games with individual (private) observations

"Illusion of control" in Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Minority game and the Parrondo Games, that agents who optimize their strategy based on past information actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in set-ups a priori defined to emphasize the importance of optimization.Comment: 17 pages, four figures, 1 tabl

A Linear Category of Polynomial Diagrams

We present a categorical model for intuitionistic linear logic where objects are polynomial diagrams and morphisms are simulation diagrams. The multiplicative structure (tensor product and its adjoint) can be defined in any locally cartesian closed category, whereas the additive (product and coproduct) and exponential Tensor-comonoid comonad) structures require additional properties and are only developed in the category Set, where the objects and morphisms have natural interpretations in terms of games, simulation and strategies.Comment: 20 page

Morphisms of open games

We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category in which the horizontal 1-cells are open games, vertical 1-morphisms are lenses, and 2-cells are morphisms of open games. States (morphisms out of the monoidal unit) in the vertical category give a flexible solution concept that includes both Nash and subgame perfect equilibria. Products in the vertical category give an external choice operator that is reminiscent of products in game semantics, and is useful in practical examples. We illustrate the above two features with a simple worked example from microeconomics, the market entry game

Unawareness in Dynamic Psychological Games

Building on Battigalli and Dufwenberg (2009)'s framework of dynamic psychological games and the recent progress in the modeling of dynamic unawareness, we provide a general framework that allows for `unawareness' in the strategic interaction of players motivated by belief-dependent psychological preferences like reciprocity and guilt. We show that unawareness has a pervasive impact on the strategic interaction of psychologically motivated players. Intuitively, unawareness influences players' beliefs concerning, for example, the intentions and expectations of others which in turn impacts their behavior. Moreover, we highlight the strategic role of communication concerning feasible paths of play in these environments.unawareness; extensive-form games; communication; belief-dependent preferences; sequential equilibrium