Related papers: On Farkas' Lemma and Related Propositions in BISH

Finding, counting, or determining the existence of Nash equilibria, where players must play optimally given each others' actions, are known to be computational intractable problems. We ask whether weakening optimality to the requirement…

We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…

We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in \cite{Kifer} in the case of a perfect market model to the case of an imperfect market with…

Fourier-Motzkin elimination, a standard method for solving systems of linear inequalities, leads to an elementary, short, and self-contained proof of von Neumann's minimax theorem.

This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some…

The equivalence between von Neumann's Minimax Theorem for zero-sum games and the LP Duality Theorem connects cornerstone problems of the two fields of game theory and optimization, respectively, and has been the subject of intense scrutiny…

This manuscript investigates the relationship between Blackwell Approachability, a stochastic vector-valued repeated game, and minimax theory, a single-play scalar-valued scenario. First, it is established in a general setting --- one not…

This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…

Game-theoretic concepts have been extensively studied in economics to provide insight into competitive behaviour and strategic decision making. As computing systems increasingly involve concurrently acting autonomous agents, game-theoretic…

This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates…

[REVISED VERSION] The aim of this paper is to state a sharp version of the K\"onig supremum theorem, an equivalent reformulation of the Hahn--Banach theorem. We apply it to derive statements of the Lagrange multipliers, Karush-Kuhn-Tucker…

The logic of the hide and seek game LHS was proposed to reason about search missions and interactions between agents in pursuit-evasion environments. As proved in literature, having an equality constant in the language of LHS drastically…

Many analysis and verifications tasks, such as static program analyses and model-checking for temporal logics reduce to the solution of systems of equations over suitable lattices. Inspired by recent work on lattice-theoretic progress…

We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…

We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…

The desirable gambles framework provides a foundational approach to imprecise probability theory but relies heavily on linear utility assumptions. This paper introduces function-coherent gambles, a generalization that accommodates…

In this paper we investigate Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games whose cost functionals are defined by a system of coupled backward stochastic differential equations. We obtain an existence…

This paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances. Our proposed distributionally robust safe policy maximizes the probability of a system remaining in a…

Many non-trivial sequential decision-making problems are efficiently solved by relying on Bellman's optimality principle, i.e., exploiting the fact that sub-problems are nested recursively within the original problem. Here we show how it…

We develop a flexible stochastic approximation framework for analyzing the long-run behavior of learning in games (both continuous and finite). The proposed analysis template incorporates a wide array of popular learning algorithms,…