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Mithun Chakraborty

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14 papers

2 author rows

AAMAS Conference 2026 Conference Paper

Computing Perfect Bayesian Equilibria, with Application to Empirical Game-Theoretic Analysis

Christine Konicki
Mithun Chakraborty
Michael P. Wellman

PerfectBayesianEquilibrium(PBE)isarefinementoftheNashequilibrium for imperfect-information extensive-form games (EFGs) that enforces consistency between the two components of a solution: agents’ strategy profile describing their decisions at information sets and the belief system quantifying their uncertainty over histories within an information set. We present a scalable approach for computing a PBE of an arbitrary two-player EFG. We adopt the definition of PBE enunciated by Bonanno in 2011 using a consistency concept based on the theory of belief revision due to Alchourrón, Gärdenfors, and Makinson. Our algorithm for finding a PBE is an adaptation of Counterfactual Regret Minimization (CFR) that minimizes the expected regret at each information set given a belief system, while maintaining the necessary consistency criteria. We prove that our algorithm is correct for two-player zerosum games and has a reasonable slowdown in time-complexity relative to classical CFR given the additional computation needed for refinement. We also experimentally demonstrate the competent performance of PBE-CFR in terms of equilibrium quality and running time on medium-to-large non-zero-sum EFGs. Finally, we investigate the effectiveness of using PBE for strategy exploration in empirical game-theoretic analysis. Specifically, we compute PBE asameta-strategysolver(MSS)inatree-exploitingvariantofPolicy Space Response Oracles (TE-PSRO). Our experiments show that PBE as an MSS leads to higher-quality empirical EFG models with complex imperfect information structures compared to MSSs based on an unrefined Nash equilibrium.

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AAMAS Conference 2025 Conference Paper

Policy Abstraction and Nash Refinement in Tree-Exploiting PSRO

Christine Konicki
Mithun Chakraborty
Michael P. Wellman

Policy Space Response Oracles (PSRO) interleaves empirical gametheoretic analysis with deep reinforcement learning (DRL) to solve games too complex for traditional analytic methods. Tree-exploiting PSRO (TE-PSRO) is a variant of this approach that iteratively builds a coarsened empirical game model in extensive form using data obtained from querying a simulator that represents a detailed description of the game. We make two main methodological advances to TE-PSRO that enhance its applicability to complex games of imperfect information. First, we introduce a scalable representation for the empirical game tree where edges correspond to implicit policies learned through DRL. These policies cover conditions in the underlying game abstracted in the game model, supporting sustainable growth of the tree over epochs. Second, we leverage extensive form in the empirical model by employing refined Nash equilibria to direct strategy exploration. To enable this, we give a modular and scalable algorithm based on generalized backward induction for computing a subgame perfect equilibrium (SPE) in an imperfect-information game. We experimentally evaluate our approach on a suite of games including an alternating-offer bargaining game with outside offers; our results demonstrate that TE-PSRO converges toward equilibrium faster when new strategies are generated based on SPE rather than Nash equilibrium, and with reasonable time/memory requirements for the growing empirical model.

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UAI Conference 2022 Conference Paper

Solving structured hierarchical games using differential backward induction

Zun Li 0002
Feiran Jia
Aditya Mate
Shahin Jabbari
Mithun Chakraborty
Milind Tambe
Yevgeniy Vorobeychik

From large-scale organizations to decentralized political systems, hierarchical strategic decision making is commonplace. We introduce a novel class of structured hierarchical games (SHGs) that formally capture such hierarchical strategic interactions. In an SHG, each player is a node in a tree, and strategic choices of players are sequenced from root to leaves, with root moving first, followed by its children, then followed by their children, and so on until the leaves. A player’s utility in an SHG depends on its own decision, and on the choices of its parent and all the tree leaves. SHGs thus generalize simultaneous-move games, as well as Stackelberg games with many followers. We leverage the structure of both the sequence of player moves as well as payoff dependence to develop a gradient-based back propagation-style algorithm, which we call Differential Backward Induction (DBI), for approximating equilibria of SHGs. We provide a sufficient condition for convergence of DBI and demonstrate its efficacy in finding approximate equilibrium solutions to several SHG models of hierarchical policy-making problems.

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AAAI Conference 2022 Conference Paper

Weighted Fairness Notions for Indivisible Items Revisited

Mithun Chakraborty
Erel Segal-Halevi
Warut Suksompong

We revisit the setting of fairly allocating indivisible items when agents have different weights representing their entitlements. First, we propose a parameterized family of relaxations for weighted envy-freeness and the same for weighted proportionality; the parameters indicate whether smallerweight or larger-weight agents should be given a higher priority. We show that each notion in these families can always be satisfied, but any two cannot necessarily be fulfilled simultaneously. We then introduce an intuitive weighted generalization of maximin share fairness and establish the optimal approximation of it that can be guaranteed. Furthermore, we characterize the implication relations between the various weighted fairness notions introduced in this and prior work, and relate them to the lower and upper quota axioms from apportionment.

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AIJ Journal 2021 Journal Article

Picking sequences and monotonicity in weighted fair division

Mithun Chakraborty
Ulrike Schmidt-Kraepelin
Warut Suksompong

We study the problem of fairly allocating indivisible items to agents with different entitlements, which captures, for example, the distribution of ministries among political parties in a coalition government. Our focus is on picking sequences derived from common apportionment methods, including five traditional divisor methods and the quota method. We paint a complete picture of these methods in relation to known envy-freeness and proportionality relaxations for indivisible items as well as monotonicity properties with respect to the resource, population, and weights. In addition, we provide characterizations of picking sequences satisfying each of the fairness notions, and show that the well-studied maximum Nash welfare solution fails resource- and population-monotonicity even in the unweighted setting. Our results serve as an argument in favor of using picking sequences in weighted fair division problems.

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IJCAI Conference 2021 Conference Paper

Picking Sequences and Monotonicity in Weighted Fair Division

Mithun Chakraborty
Ulrike Schmidt-Kraepelin
Warut Suksompong

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IJCAI Conference 2019 Conference Paper

Fairness Towards Groups of Agents in the Allocation of Indivisible Items

Nawal Benabbou
Mithun Chakraborty
Edith Elkind
Yair Zick

In this paper, we study the problem of matching a set of items to a set of agents partitioned into types so as to balance fairness towards the types against overall utility/efficiency. We extend multiple desirable properties of indivisible goods allocation to our model and investigate the possibility and hardness of achieving combinations of these properties, e. g. we prove that maximizing utilitarian social welfare under constraints of typewise envy-freeness up to one item (TEF1) is computationally intractable. We also define a new concept of waste for this setting, show experimentally that augmenting an existing algorithm with a marginal utility maximization heuristic can produce a TEF1 solution with reduced waste, and also provide a polynomial-time algorithm for computing a non-wasteful TEF1 allocation for binary agent-item utilities.

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AAMAS Conference 2018 Conference Paper

Diversity Constraints in Public Housing Allocation

Nawal Benabbou
Mithun Chakraborty
Xuan-Vinh Ho
Jakub Sliwinski
Yair Zick

The state of Singapore operates a national public housing program, accounting for over 70% of its residential real estate. Singapore uses its housing allocation program to promote ethnic diversity in its neighborhoods; it does so by imposing ethnic quotas: every ethnic group must not own more than a certain percentage in a housing project, thus ensuring that every neighborhood contains members from each ethnic group. However, imposing diversity constraints naturally results in some welfare loss. Our work studies the tradeoff between diversity and (utilitarian) social welfare from the perspective of computational economics. We model the problem as an extension of the classic assignment problem, with additional diversity constraints. While the classic assignment program is polytime computable, we show that adding diversity constraints makes the problem computationally intractable; however, we identify a 1 2 approximation algorithm, as well as reasonable agent utility models which admit poly-time algorithms. In addition, we study the price of diversity: this is the loss in welfare incurred by imposing diversity constraints; we provide upper bounds on the price of diversity as functions of natural problem parameters. Finally, we use recent, public demographic and real-estate data from Singapore to create a simulated framework testing the welfare loss due to diversity constraints in realistic large-scale scenarios.

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IJCAI Conference 2017 Conference Paper

Coordinated Versus Decentralized Exploration In Multi-Agent Multi-Armed Bandits

Mithun Chakraborty
Kai Yee Phoebe Chua
Sanmay Das
Brendan Juba

In this paper, we introduce a multi-agent multi-armed bandit-based model for ad hoc teamwork with expensive communication. The goal of the team is to maximize the total reward gained from pulling arms of a bandit over a number of epochs. In each epoch, each agent decides whether to pull an arm, or to broadcast the reward it obtained in the previous epoch to the team and forgo pulling an arm. These decisions must be made only on the basis of the agent’s private information and the public information broadcast prior to that epoch. We first benchmark the achievable utility by analyzing an idealized version of this problem where a central authority has complete knowledge of rewards acquired from all arms in all epochs and uses a multiplicative weights update algorithm for allocating arms to agents. We then introduce an algorithm for the decentralized setting that uses a value-of-information based communication strategy and an exploration-exploitation strategy based on the centralized algorithm, and show experimentally that it converges rapidly to the performance of the centralized method.

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IJCAI Conference 2016 Conference Paper

Trading on a Rigged Game: Outcome Manipulation in Prediction Markets

Mithun Chakraborty
Sanmay Das

Prediction markets are popular mechanisms for aggregating information about a future event. In situations where market participants may significantly influence the outcome, running the prediction market could change the incentives of participants in the process that creates the outcome. We propose a new game-theoretic model that captures two aspects of real-world prediction markets: (1) agents directly affect the outcome the market is predicting, (2) some outcome-deciders may not participate in the market. We show that this game has two types of equilibria: When some outcome-deciders are unlikely to participate in the market, equilibrium prices reveal expected market outcomes conditional on participants' private information, whereas when all outcome-deciders are likely to participate, equilibria are collusive - agents effectively coordinate in an uninformative and untruthful way.

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NeurIPS Conference 2015 Conference Paper

Market Scoring Rules Act As Opinion Pools For Risk-Averse Agents

Mithun Chakraborty
Sanmay Das

A market scoring rule (MSR) – a popular tool for designing algorithmic prediction markets – is an incentive-compatible mechanism for the aggregation of probabilistic beliefs from myopic risk-neutral agents. In this paper, we add to a growing body of research aimed at understanding the precise manner in which the price process induced by a MSR incorporates private information from agents who deviate from the assumption of risk-neutrality. We first establish that, for a myopic trading agent with a risk-averse utility function, a MSR satisfying mild regularity conditions elicits the agent’s risk-neutral probability conditional on the latest market state rather than her true subjective probability. Hence, we show that a MSR under these conditions effectively behaves like a more traditional method of belief aggregation, namely an opinion pool, for agents’ true probabilities. In particular, the logarithmic market scoring rule acts as a logarithmic pool for constant absolute risk aversion utility agents, and as a linear pool for an atypical budget-constrained agent utility with decreasing absolute risk aversion. We also point out the interpretation of a market maker under these conditions as a Bayesian learner even when agent beliefs are static.

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AAAI Conference 2015 Conference Paper

Price Evolution in a Continuous Double Auction Prediction Market With a Scoring-Rule Based Market Maker

Mithun Chakraborty
Sanmay Das
Justin Peabody

The logarithmic market scoring rule (LMSR), the most common automated market making rule for prediction markets, is typically studied in the framework of dealer markets, where the market maker takes one side of every transaction. The continuous double auction (CDA) is a much more widely used microstructure for general financial markets in practice. In this paper, we study the properties of CDA prediction markets with zerointelligence traders in which an LMSR-style market maker participates actively. We extend an existing idea of Robin Hanson for integrating LMSR with limit order books in order to provide a new, self-contained market making algorithm that does not need “special” access to the order book and can participate as another trader. We find that, as expected, the presence of the market maker leads to generally lower bid-ask spreads and higher trader surplus (or price improvement), but, surprisingly, does not necessarily improve price discovery and market efficiency; this latter effect is more pronounced when there is higher variability in trader beliefs.

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AAAI Conference 2013 Conference Paper

Instructor Rating Markets

Mithun Chakraborty
Sanmay Das
Allen Lavoie
Malik Magdon-Ismail
Yonatan Naamad

We describe the design of Instructor Rating Markets (IRMs) where human participants interact through intelligent automated market-makers in order to provide dynamic collective feedback to instructors on the progress of their classes. The markets are among the first to enable the empirical study of prediction markets where traders can affect the very outcomes they are trading on. More than 200 students across the Rensselaer campus participated in markets for ten classes in the Fall 2010 semester. In this paper, we describe how we designed these markets in order to elicit useful information, and analyze data from the deployment. We show that market prices convey useful information on future instructor ratings and contain significantly more information than do past ratings. The bulk of useful information contained in the price of a particular class is provided by students who are in that class, showing that the markets are serving to disseminate insider information. At the same time, we find little evidence of attempted manipulation by raters. The markets are also a laboratory for comparing different market designs and the resulting price dynamics, and we show how they can be used to compare market making algorithms.

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UAI Conference 2011 Conference Paper

Near-Optimal Target Learning With Stochastic Binary Signals

Mithun Chakraborty
Sanmay Das
Malik Magdon-Ismail

We study learning in a noisy bisection model: specifically, Bayesian algorithms to learn a target value V given access only to noisy realizations of whether V is less than or greater than a threshold theta. At step t = 0, 1, 2, ..., the learner sets threshold theta t and observes a noisy realization of sign(V - theta t). After T steps, the goal is to output an estimate V^ which is within an eta-tolerance of V . This problem has been studied, predominantly in environments with a fixed error probability q V , and there is little known when this happens. We give a pseudo-Bayesian algorithm which provably converges to V. When the true prior matches our algorithm's Gaussian prior, we show near-optimal expected performance. Our methods extend to the general multiple-threshold setting where the observation noisily indicates which of k >= 2 regions V belongs to.

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