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We compare games under delayed control and delay games, two types of infinite games modelling asynchronicity in reactive synthesis. Our main result, the interreducibility of the existence of sure winning strategies for the protagonist,…
Prisoner's dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on…
Motivated by the fact that the same social dilemma can be perceived differently by different players, we here study evolutionary multigames in structured populations. While the core game is the weak prisoner's dilemma, a fraction of the…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
Iterated games provide a framework to describe social interactions among groups of individuals. Recent work stimulated by the discovery of "zero-determinant" strategies has rapidly expanded our ability to analyze such interactions. This…
It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals…
At the beginning of a dynamic game, players may have exogenous theories about how the opponents are going to play. Suppose that these theories are commonly known. Then, players will refine their first-order beliefs, and challenge their own…
Recently, the eco-evolutionary game theory which describes the coupled dynamics of strategies and environment have attracted great attention. At the same time, most of the current work is focused on the classic two-player two-strategy game.…
Differential game logic (dGL) is a logic for specifying and verifying properties of hybrid games, i.e. games that combine discrete, continuous, and adversarial dynamics. Unlike hybrid systems, hybrid games allow choices in the system…
We propose an evolutionary coordination game to formalize a simplified model of the evolution of strategies during human courtship. The dynamics, derived from the consideration of experimental observations on human social behavior driven by…
The effects of an additional strategy or character called loner in the snowdrift game are studied in a well-mixed population or fully-connected network and in a square lattice. The snowdrift game, which is a possible alternative to the…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…
Reinforcement Learning and the Evolutionary Strategy are two major approaches in addressing complicated control problems. Both are strong contenders and have their own devotee communities. Both groups have been very active in developing new…
In the evolutionary minority game, agents are allowed to evolve their strategies (``mutate'') based on past experience. We explore the dependence of the system's global behavior on the response time and the mutation threshold of the agents.…
We consider a class of zero-sum stopper vs. singular-controller games in which the controller can only act on a subset $d_0<d$ of the $d$ coordinates of a controlled diffusion. Due to the constraint on the control directions these games…
Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
Indirect reciprocity is one of the main mechanisms to explain the emergence and sustainment of altruism in societies. The standard approach to indirect reciprocity are reputation models. These are games in which players base their decisions…
Dynamics in a distributed system are self-stabilizing if they are guaranteed to reach a stable state regardless of how the system is initialized. Game dynamics are uncoupled if each player's behavior is independent of the other players'…