Hasil untuk "cs.GT"

Jason Hartline

This brief note clarifies that the scenario described in Arunachaleswaran et al. (2025) -- titled `Algorithmic Collusion without Threats' -- is not one of collusion, but one where one player is behaving non-competitively and the other is behaving competitively.

Edan Orzech, Martin Rinard

We present for every $n\ge4$ an $n$-player game in normal form with payoffs in $\{0,1,2\}$ that has a unique, fully mixed, Nash equilibrium in which all the probability weights are irradical (i.e., algebraic but not closed form expressible even with $m$-th roots for any integer $m$).

Niclas Boehmer, Robert Bredereck, Piotr Faliszewski et al.

We study the parameterized complexity of counting variants of Swap- and Shift-Bribery problems, focusing on the parameterizations by the number of swaps and the number of voters. We show experimentally that Swap-Bribery offers a new approach to the robustness analysis of elections.

Haris Aziz

It is standard in computational social choice to analyse welfare considerations under the assumptions of normalized utilities. In this note, we summarize some common reasons for this approach. We then mention another justification which is ignored but has solid normative appeal. The central concept used in the `new' justification can also be used more widely as a social objective.

Ron Kupfer

We consider the problem of maximizing revenue when selling k items to a single buyer with known valuation distributions. We show that for a single, additive buyer whose valuations for for the items are distributed according to i.i.d. distributions which are known to the seller, the ratio of revenue from selling in a bundle to selling separately is at least 55.9% and this gap is attainable.

Joseph Y. Halpern, Yoram Moses

Characterizations of Nash equilibrium, correlated equilibrium, and rationalizability in terms of common knowledge of rationality are well known. Analogous characterizations of sequential equilibrium, (trembling hand) perfect equilibrium, and quasi-perfect equilibrium using results of Halpern [2009].

Egor Ianovski

The Duggan-Schwartz theorem (Duggan and Schwartz, 1992) is a famous result concerning strategy-proof social choice correspondences, often stated as "A social choice correspondence that can be manipulated by neither an optimist nor a pessimist has a weak dictator". However, this formulation is actually due to Taylor (2002), and the original theorem, at face value, looks rather different. In this note we show that the two are in fact equivalent.

Shahar Dobzinski, Ami Mor

In this note we study the greedy algorithm for combinatorial auctions with submodular bidders. It is well known that this algorithm provides an approximation ratio of $2$ for every order of the items. We show that if the valuations are vertex cover functions and the order is random then the expected approximation ratio imrpoves to $\frac 7 4$.

Egor Ianovski

We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean game G determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in Feigenbaum et al. (1995).

Sascha Kurz

The design of fair voting rules has been addressed quite often in the literature. Still, the so-called inverse problem is not entirely resolved. We summarize some achievements in this direction and formulate explicit open questions and conjectures.

Guanglei He, Zhihui Qin

Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction games. In addition, it is much simpler than Sprague-Grundy Theory in one pile of the games.

Glenn C. Rhoads, Laurent Bartholdi

We solve the classical "Game of Pure Strategy" using linear programming. We notice an intricate even-odd behavior in the results of our computations, that seems to encourage odd or maximal bids.

Egor Ianovski

We examine the history of cake cutting mechanisms and discuss the efficiency of their allocations. In the case of piecewise uniform preferences, we define a game that in the presence of strategic agents has equilibria that are not dominated by the allocations of any mechanism. We identify that the equilibria of this game coincide with the allocations of an existing cake cutting mechanism.

Hamadene Said, Hassani Mohammed

In this paper we study the N-player nonzero-sum Dynkin game ($N\geq 3$) in continuous time, which is a non-cooperative game where the strategies are stopping times. We show that the game has a Nash equilibrium point for general payoff processes.

Can Baskent

In this paper, we discuss a well-known self-referential paradox in foundational game theory, the Brandenburger - Keisler paradox. We approach the paradox from two different perspectives: non-well-founded set theory and paraconsistent logic. We show that the paradox persists in both frameworks for category theoretical reasons, but, with different properties.

David Auger

We propose an algorithm for computing approximate Nash equilibria of partially observable games using Monte-Carlo tree search based on recent bandit methods. We obtain experimental results for the game of phantom tic-tac-toe, showing that strong strategies can be efficiently computed by our algorithm.

Krishnendu Chatterjee, Rupak Majumdar, Thomas A. Henzinger

The value of a finite-state two-player zero-sum stochastic game with limit-average payoff can be approximated to within $ε$ in time exponential in a polynomial in the size of the game times polynomial in logarithmic in $\frac{1}ε$, for all $ε>0$.

Nathalie Bertrand, Blaise Genest, Hugo Gimbert

We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions.

Thierry Cachat

We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new representation of (sets of) ordinals by (infinite) trees.

Thierry Cachat

Ordinal automata are used to model physical systems with Zeno behavior. Using automata and games techniques we solve a control problem formulated and left open by Demri and Nowak in 2005. It involves partial observability and a new synchronization between the controller and the environment.