Bayesian Exploration: Incentivizing Exploration in Bayesian Games

In a wide range of recommendation systems, self-interested individuals (“agents”) make decisions over time, using information revealed by other agents in the past, and producing information that may help agents in the future. Each agent would like to exploit the best action given the current information but would prefer the previous agents to explore various alternatives to collect information. A social planner, by means of a well-designed recommendation policy, can incentivize the agents to balance exploration and exploitation in order to maximize social welfare or some other objective. The recommendation policy can be modeled as a multiarmed bandit algorithm under Bayesian incentivecompatibility (BIC) constraints. This line of work has received considerable attention in the “economics and computation” community. Although in prior work, the planner interacts with a single agent at a time, the present paper allows the agents to affect one another directly in a shared environment. The agents now face two sources of uncertainty: what is the environment, and what would the other agents do? We focus on “explorable” actions: those that can be recommended by some BIC policy. We show how the principal can identify and explore all such actions.

Delegation Using Forward Induction

This paper explores how delegation can be used as a signal to sustain cooperation. I consider a static principal–agent model with two tasks, one resembling a coordination game. If there is asymmetric information about the agent’s type, the principal with high private belief can delegate the first task as a signal. This is also supported by the forward induction argument. However, in the laboratory setting, this equilibrium is chosen only sometimes. When the subjects have information about past sessions, there is a significant increase in the use of delegation. This finding sheds light on equilibrium selection in Bayesian games.

Equilibria Existence in Bayesian Games: Climbing the Countable Borel Equivalence Relation Hierarchy

The solution concept of a Bayesian equilibrium of a Bayesian game is inherently an interim concept. The corresponding ex ante solution concept has been termed a Harsányi equilibrium; examples have appeared in the literature showing that there are Bayesian games with uncountable state spaces that have no Bayesian approximate equilibria but do admit a Harsányi approximate equilibrium, thus exhibiting divergent behaviour in the ex ante and interim stages. Smoothness, a concept from descriptive set theory, has been shown in previous works to guarantee the existence of Bayesian equilibria. We show here that higher rungs in the countable Borel equivalence relation hierarchy can also shed light on equilibrium existence. In particular, hyperfiniteness, the next step above smoothness, is a sufficient condition for the existence of Harsányi approximate equilibria in purely atomic Bayesian games.

Brazilian Evidence on Tax Evasion and Enforcement: A Case Study of Global North–South Comparison

This study investigates the differences observed in the rate of tax evasion between the Global North and South countries, with special focus on Brazil, by comparing key parameters of their tax systems, namely, tax burden, audit cost, and fines. This is achieved by extending and applying Graetz, Reinganun, and Wilde’s model using data from tax authorities from European and Latin American countries, which produced parameters that are used for Bayesian games. The results show that tax evasion is directly associated with tax burden and audit cost, but the effect of fines is unclear. Overall, findings pointed to shortcomings in the tax system of Latin American countries that create the avenue for high tax evasion.

Game-Theoretic Decision Support for Cyber Forensic Investigations

The use of anti-forensic techniques is a very common practice that stealthy adversaries may deploy to minimise their traces and make the investigation of an incident harder by evading detection and attribution. In this paper, we study the interaction between a cyber forensic Investigator and a strategic Attacker using a game-theoretic framework. This is based on a Bayesian game of incomplete information played on a multi-host cyber forensics investigation graph of actions traversed by both players. The edges of the graph represent players’ actions across different hosts in a network. In alignment with the concept of Bayesian games, we define two Attacker types to represent their ability of deploying anti-forensic techniques to conceal their activities. In this way, our model allows the Investigator to identify the optimal investigating policy taking into consideration the cost and impact of the available actions, while coping with the uncertainty of the Attacker’s type and strategic decisions. To evaluate our model, we construct a realistic case study based on threat reports and data extracted from the MITRE ATT&CK STIX repository, Common Vulnerability Scoring System (CVSS), and interviews with cyber-security practitioners. We use the case study to compare the performance of the proposed method against two other investigative methods and three different types of Attackers.

Temporal Induced Self-Play for Stochastic Bayesian Games

One practical requirement in solving dynamic games is to ensure that the players play well from any decision point onward. To satisfy this requirement, existing efforts focus on equilibrium refinement, but the scalability and applicability of existing techniques are limited. In this paper, we propose Temporal-Induced Self-Play (TISP), a novel reinforcement learning-based framework to find strategies with decent performances from any decision point onward. TISP uses belief-space representation, backward induction, policy learning, and non-parametric approximation. Building upon TISP, we design a policy-gradient-based algorithm TISP-PG. We prove that TISP-based algorithms can find approximate Perfect Bayesian Equilibrium in zero-sum one-sided stochastic Bayesian games with finite horizon. We test TISP-based algorithms in various games, including finitely repeated security games and a grid-world game. The results show that TISP-PG is more scalable than existing mathematical programming-based methods and significantly outperforms other learning-based methods.

Robustness of Equilibria in Anonymous Local Games

This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class.