Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Online Networks, Social Interaction and Segregation: An Evolutionary Approach

We have developed an evolutionary game model, where agents can choose between two forms of social participation: interaction via online social networks and interaction by exclusive means of face-to-face encounters. We illustrate the societal dynamics that the model predicts, in light of the empirical evidence provided by previous literature. We then assess their welfare implications. We show that dynamics, starting from a world in which online social interaction is less gratifying than offline encounters, will lead to the extinction of the sub-population of online networks users, thereby making Facebook and alike disappear in the long run. Furthermore, we show that the higher the propensity for discrimination between the two sub-populations of socially active individuals, the greater the probability that individuals will ultimately segregate themselves, making society fall into a social poverty trap

On Nash-Solvability of Finite Two-Person Tight Vector Game Forms

We consider finite two-person normal form games. The following four properties of their game forms are equivalent: (i) Nash-solvability, (ii) zero-sum-solvability, (iii) win-lose-solvability, and (iv) tightness. For (ii, iii, iv) this was shown by Edmonds and Fulkerson in 1970. Then, in 1975, (i) was added to this list and it was also shown that these results cannot be generalized for $n$-person case with $n > 2$. In 1990, tightness was extended to vector game forms ($v$-forms) and it was shown that such $v$-tightness and zero-sum-solvability are still equivalent, yet, do not imply Nash-solvability. These results are applicable to several classes of stochastic games with perfect information. Here we suggest one more extension of tightness introducing $v^+$-tight vector game forms ($v^+$-forms). We show that such $v^+$-tightness and Nash-solvability are equivalent in case of weakly rectangular game forms and positive cost functions. This result allows us to reduce the so-called bi-shortest path conjecture to $v^+$-tightness of $v^+$-forms. However, both (equivalent) statements remain open

Counterfactual Regret Minimization を用いたトレーディングカードゲームの戦略計算

学位の種別: 修士University of Tokyo(東京大学