It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization of strategy complexity, Rubinstein and co-authors studied forms of Nash equilibrium where strategies are maximally simplified in that no strategy can be further simplified without sacrificing payoff. Inspired by this line of work, we introduce a notion of equilibrium whereby strategies are also maximally simplified, but with respect to a simplification procedure that is more careful in that a player will not simplify if the simplification incents other players to deviate. We study such equilibria in two-player machine games in which players choose finite automata that succinctly represent strategies for repeated games; in this context, we present techniques for establishing that an outcome is at equilibrium and present results on the structure of equilibria.
We investigate the effect of information asymmetry on a dynamic Cournot duopoly game with bounded rationality. Concretely, we study how one player's possession of information about the other player's behavior in a duopoly affects the stability of the Cournot-Nash equilibrium. We theoretically and numerically show that the information stabilizes the Cournot-Nash equilibrium and suppresses chaotic behavior in the duopoly.
From the standpoint of game theory, dominoes is a game that has not received much attention (specially the variety known as draw). It is usually thought that this game is already solved, given general results in game theory. However, the determination of equilibria is not feasible for the general case because of the well known problem of node explosion in the tree expressing the game. We propose a new model based in limited forecast as a kind of bounded rationality for dynamic alternate games.
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem -- instead of prescribing equilibrium of a given game, we may directly observe the agents' equilibrium behaviors but want to infer the underlying parameters of an unknown game. This research question, also known as inverse game theory, has been studied in multiple recent works in the context of Stackelberg games. Unfortunately, existing works exhibit quite negat…
In multimedia crowdsourcing, the requester's quality requirements and reward decisions will affect the workers' task selection strategies and the quality of their multimedia contributions. In this paper, we present a first study on how the workers' bounded cognitive rationality interacts with and affects the decisions and performance of a multimedia crowdsourcing system. Specifically, we consider a two-stage model, where a requester first determines the reward and the quality requirement for each task, and the workers select the tasks to accomplish accordingly. First, we consider the benchmark…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the hardness of factoring. We define a new notion of bounded rationality, where the payoffs of players are discounted by the computation time they take to produce their actions. We use this notion to give a direct correspondence between the existence of equilibria where Alice has a winning strategy and the hardness of factoring. Namely, under a natural assumption …
The paper proposes a novel neuroevolutionary method (NESG) for calculating leader's payoff in Stackelberg Security Games. The heart of NESG is strategy evaluation neural network (SENN). SENN is able to effectively evaluate leader's strategies against an opponent who may potentially not behave in a perfectly rational way due to certain cognitive biases or limitations. SENN is trained on historical data and does not require any direct prior knowledge regarding the follower's target preferences, payoff distribution or bounded rationality model. NESG was tested on a set of 90 benchmark games inspi…
Singapore University of Technology and Design（新加坡科技设计大学）；University of Oxford（牛津大学）
The interplay between exploration and exploitation in competitive multi-agent learning is still far from being well understood. Motivated by this, we study smooth Q-learning, a prototypical learning model that explicitly captures the balance between game rewards and exploration costs. We show that Q-learning always converges to the unique quantal-response equilibrium (QRE), the standard solution concept for games under bounded rationality, in weighted zero-sum polymatrix games with heterogeneous learning agents using positive exploration rates. Complementing recent results about convergence in…
Classic decision-theory is based on the maximum expected utility (MEU) principle, but crucially ignores the resource costs incurred when determining optimal decisions. Here we propose an axiomatic framework for bounded decision-making that considers resource costs. Agents are formalized as probability measures over input-output streams. We postulate that any such probability measure can be assigned a corresponding conjugate utility function based on three axioms: utilities should be real-valued, additive and monotonic mappings of probabilities. We show that these axioms enforce a unique conver…
In this paper, a general model for cyber-physical systems (CPSs), that captures the diffusion of attacks from the cyber layer to the physical system, is studied. In particular, a game-theoretic approach is proposed to analyze the interactions between one defender and one attacker over a CPS. In this game, the attacker launches cyber attacks on a number of cyber components of the CPS to maximize the potential harm to the physical system while the system operator chooses to defend a number of cyber nodes to thwart the attacks and minimize potential damage to the physical side. The proposed game …
We consider 2-player games played on a finite state space for infinite rounds. The games are concurrent: in each round, the two players choose their moves simultaneously; the current state and the moves determine the successor. We consider omega-regular winning conditions given as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require…
Despite the emphases on computability issues in research of algorithmic game theory, the limited computational capacity of players have received far less attention. This work examines how different levels of players' computational ability (or "rationality") impact the outcomes of sequential scheduling games. Surprisingly, our results show that a lower level of rationality of players may lead to better equilibria. More specifically, we characterize the sequential price of anarchy (SPoA) under two different models of bounded rationality, namely, players with $k$-lookahead and simple-minded playe…
While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the Quantal Hierarchy model, which can relax both mutual consistency and best response while still approximating level-$k$, QRE…
A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principled formulation of bounded rationality and a set of new types of mean field theory in statistical …
Incorporating Bounded Rationality into Electric Vehicle Highway Charging Decisions: A Bayesian Game Analysis
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）；Shenzhen Key Laboratory of Crowd Intelligence Empowered Low-Carbon Energy Network（深圳市 crowd intelligence 赋能低碳能源网络重点实验室）
Congestion games model a wide variety of real-world resource congestion problems, such as selfish network routing, traffic route guidance in congested areas, taxi fleet optimization and crowd movement in busy areas. However, existing research in congestion games assumes: (a) deterministic movement of agents between resources; and (b) perfect rationality (i.e. maximizing their own expected value) of all agents. Such assumptions are not reasonable in dynamic domains where decision support has to be provided to humans. For instance, in optimizing the performance of a taxi fleet serving a city, mo…
An underlying assumption of Stackelberg Games (SGs) is perfect rationality of the players. However, in real-life situations (which are often modeled by SGs) the followers (terrorists, thieves, poachers or smugglers) -- as humans in general -- may act not in a perfectly rational way, as their decisions may be affected by biases of various kinds which bound rationality of their decisions. One of the popular models of bounded rationality (BR) is Anchoring Theory (AT) which claims that humans have a tendency to flatten probabilities of available options, i.e. they perceive a distribution of these …
