It is known that the set of all correlated equilibria of an [Formula: see text]-player non-cooperative game is a convex polytope and includes all of the Nash equilibria. Furthermore, 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 of the CPT Nash equilibria, but it need not be a convex polytope. We show that it can, in fact, be disconnected. However, all of 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 [Formula: see text] games, with the sets of correlated and Nash equilibria in the classical sense being a special case.

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Serverless computing platforms currently rely on basic pricing schemes that are static and do not reflect customer feedback. This leads to significant inefficiencies from a total utility perspective. As one of the fastest-growing cloud services, serverless computing provides an opportunity to better serve both users and providers through the incorporation of market-based strategies for pricing and resource allocation. With the help of utility functions to model the delay-sensitivity of customers, we propose a novel scheduler to allocate resources for serverless computing. The resulting resource allocation scheme is optimal in the sense that it maximizes the aggregate utility of all users across the system, thus maximizing social welfare. Our approach gives rise to a dynamic pricing scheme which is obtained by solving an optimization problem in its dual form. We further develop feedback mechanisms that allow the cloud provider to converge to optimal resource allocation, even when the users' utilities are unknown. Simulations show that our approach can track market demand and achieve significantly higher social welfare (or, equivalently, cost savings for customers) as compared to existing schemes.

We consider repeated games where players behave according to cumulative prospect theory (CPT). We show that a natural analog for 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 when players have calibrated strategies and behave according to CPT. We define the notion of a mediated CPT correlated equilibrium via an extension of the game to a so-called mediated game. We then show, along the lines of Foster and Vohra's result, that 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 mediated games are a specific type of games with communication introduced by Myerson, and as a consequence we get that the revelation principle does not hold under CPT.

It is known that the set of all correlated equilibria of an n-player noncooperative 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 2 × 2 games.