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This paper studies the rational synthesis problem for multi-player games played on graphs when rational players are following subgame perfect equilibria. In these games, one player, the system, declares his strategy upfront, and the other…

Based on an exact functional form derived for the three-point vertex function $\Gamma$, we propose a self-consistent calculation scheme for the electron self-energy with $\Gamma$ always satisfying the Ward identity. This scheme is basically…

We conduct a comprehensive analysis of the discrete-time exponential-weights dynamic with a constant step size on all general-sum and symmetric $2 \times 2$ normal-form games, i.e. games with $2$ pure strategies per player, and where the…

In empirical game-theoretic analysis (EGTA), game models are extended iteratively through a process of generating new strategies based on learning from experience with prior strategies. The strategy exploration problem in EGTA is how to…

Computing approximate Nash equilibria in multi-player general-sum Markov games is a computationally intractable task. However, multi-player Markov games with certain cooperative or competitive structures might circumvent this…

The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved…

A \emph{bidding} game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the…

Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…

Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of $\omega$-regular winning conditions; e.g., safety, reachability,…

Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the…

RSA exponent reduction and AES S-box inversion share a hidden commonality: both are governed by the same impartial combinatorial principle, which we call a Product-Congruence Game (PCG). A Product-Congruence Game tracks play via the modular…

We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of $\omega$-regular objectives, due to its relation to many…

We study the algorithm of Gurvich, Khachyian and Karzanov (GKK algorithm) when it is ran over mean-payoff games with no simple cycle of weight zero. We propose a new symmetric analysis, lowering the $O(n^2 N)$ upper-bound of Pisaruk on the…

We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past…

Reactive synthesis is a class of methods to construct a provably-correct control system, referred to as a robot, with respect to a temporal logic specification in the presence of a dynamic and uncontrollable environment. This is achieved by…

We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…

We study the problem of finding Stackelberg equilibria in games with a massive number of players. So far, the only known game instances in which the problem is solved in polynomial time are some particular congestion games. However, a…

Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic external influence. This…

Due to the spectrum reuse in small cell network, the inter-cell interference has great effect on MEC's performance. In this paper, for reducing the energy consumption and latency of MEC, we propose a game theory based jointing offloading…

This paper rethinks Sharpness-Aware Minimization (SAM), which is originally formulated as a zero-sum game where the weights of a network and a bounded perturbation try to minimize/maximize, respectively, the same differentiable loss. To…