arXiv subjects

Soham R. Phade

Publications and source records attributed to Soham R. Phade.

5 recordsLinked to original sources

arXiv2021

Mechanism Design for Cumulative Prospect Theoretic Agents: A General Framework and the Revelation Principle

This paper initiates a discussion of mechanism design when the participating agents exhibit preferences that deviate from expected utility theory (EUT). In particular, we consider mechanism design for systems where the agents are modeled as having cumulative prospect theory (CPT) preferences, which is a generalization of EUT preferences. We point out some of the key modifications needed in the theory of mechanism design that arise from agents having CPT preferences and some of the shortcomings of the classical mechanism design framework. In particular, we show that the revelation principle, which has traditionally played a fundamental role in mechanism design, does not continue to hold under CPT. We develop an appropriate framework that we call mediated mechanism design which allows us to recover the revelation principle for CPT agents. We conclude with some interesting directions for future work.

cs.GT↗

arXiv2020

Learning in Games with Cumulative Prospect Theoretic Preferences

We consider repeated games where the players behave according to cumulative prospect theory (CPT). We show that, when the players have calibrated strategies and behave according to CPT, the natural analog of the notion of correlated equilibrium in the CPT case, as defined by Keskin, is not enough to capture all subsequential limits of the empirical distribution of action play. We define the notion of a mediated CPT correlated equilibrium via an extension of the stage game to a so-called mediated game. We then show, along the lines of the result of Foster and Vohra about convergence to the set of correlated equilibria when the players behave according to expected utility theory that, in the CPT case, under calibrated learning the empirical distribution of action play converges to the set of all mediated CPT correlated equilibria. We also show that, in general, the set of CPT correlated equilibria is not approachable in the Blackwell approachability sense. We observe that a mediated game is a specific type of a game with communication, as introduced by Myerson, and as a consequence we get that the revelation principle does not hold under CPT.

cs.GT↗

arXiv2020

Black-Box Strategies and Equilibrium for Games with Cumulative Prospect Theoretic Players

The betweenness property of preference relations states that a probability mixture of two lotteries should lie between them in preference. It is a weakened form of the independence property and hence satisfied in expected utility theory (EUT). Experimental violations of betweenness are well-documented and several preference theories, notably cumulative prospect theory (CPT), do not satisfy betweenness. We prove that CPT preferences satisfy betweenness if and only if they conform with EUT preferences. In game theory, lack of betweenness in the players' preference relations makes it essential to distinguish between the two interpretations of a mixed action by a player - conscious randomizations by the player and the uncertainty in the beliefs of the opponents. We elaborate on this distinction and study its implication for the definition of Nash equilibrium. This results in four different notions of equilibrium, with pure and mixed action Nash equilibrium being two of them. We dub the other two pure and mixed black-box strategy Nash equilibrium respectively. We resolve the issue of existence of such equilibria and examine how these different notions of equilibrium compare with each other.

econ.TH↗

arXiv2018

Optimal Resource Allocation over Networks via Lottery-Based Mechanisms

We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization problem, called the system problem, to find the optimal lottery allocation. The system problem exhibits a two-layer structure comprised of a permutation profile and optimal allocations given the permutation profile. For any fixed permutation profile, we provide a market-based mechanism to find the optimal allocations and prove the existence of equilibrium prices. We show that the system problem has a duality gap, in general, and that the primal problem is NP-hard. We then consider a relaxation of the system problem and derive some qualitative features of the optimal lottery structure.

econ.TH↗

arXiv2017

On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences

It is known that the set of all correlated equilibria of an n-player non-cooperative game is a convex polytope and includes all the Nash equilibria. Further, the Nash equilibria all lie on the boundary of this polytope. We study the geometry of both these equilibrium notions when the players have cumulative prospect theoretic (CPT) preferences. The set of CPT correlated equilibria includes all the CPT Nash equilibria but it need not be a convex polytope. We show that it can, in fact, be disconnected. However, all the CPT Nash equilibria continue to lie on its boundary. We also characterize the sets of CPT correlated equilibria and CPT Nash equilibria for all 2x2 games.

cs.GT↗