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We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

We consider a game-theoretic setting to model the interplay between attacker and defender in the context of information flow, and to reason about their optimal strategies. In contrast with standard game theory, in our games the utility of a…

We apply Blackwell optimality to repeated games. An equilibrium whose strategy profile is sequentially rational for all high enough discount factors simultaneously is a Blackwell (subgame-perfect, perfect public, etc.) equilibrium. The bite…

Resource allocation problems across multiple contests are ubiquitous in adversarial settings, from military operations to market competition. While Colonel Blotto and General Lotto games have provided valuable theoretical foundations for…

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be…

Correlated equilibria -- and their generalization $\Phi$-equilibria -- are a fundamental object of study in game theory, offering a more tractable alternative to Nash equilibria in multi-player settings. While computational aspects of…

We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are…

We introduce an interactive market setup with sequential auctions where agents receive variegated signals with a known deadline. The effects of differential information and mutual learning on the allocation of overall profit \& loss (P\&L)…

The General Lotto game is a popular variant of the famous Colonel Blotto game, in which two opposing players allocate limited resources over many battlefields. In this paper, we consider incomplete and asymmetric information formulations…

We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…

We study the value and the optimal strategies for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our Bayesian set-up, the drift of the underlying diffusion process is unknown to one player…

AI algorithms for imperfect-information games are typically compared using performance metrics on individual games, making it difficult to assess robustness across game choices. Card games are a natural domain for imperfect information due…

In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has…

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning…

Sequential equilibrium is the conventional approach for analyzing multi-stage games of incomplete information. It relies on mutual consistency of beliefs. To relax mutual consistency, I theoretically and experimentally explore the dynamic…

We extend to the multi-asset case the framework of a discrete time model of a single asset financial market developed in Ghoulmie et al (2005). In particular, we focus on adaptive agents with threshold behavior allocating their resources…

Players are statistical learners who learn about payoffs from data. They may interpret the same data differently, but have common knowledge of a class of learning procedures. I propose a metric for the analyst's "confidence" in a strategic…

A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…