Search results for "Combinatorial game theory"
showing 10 items of 13 documents
Strategic Thinking under social influence: Scalability, stability and robustness of allocations
2016
This paper studies the strategic behavior of a large number of game designers and studies the scalability, stability and robustness of their allocations in a large number of homogeneous coalitional games with transferable utilities (TU). For each TU game, the characteristic function is a continuous-time stochastic process. In each game, a game designer allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. The approach is based on the theory of mean-field games with heterogeneous groups in a multi-population regime.
Robust Allocation Rules in Dynamical Cooperative TU Games
2011
Robust dynamic coalitional TU games are repeated TU games where the values of the coalitions are unknown but bounded variables. We set up the game supposing that the Game Designer uses a vague measure of the extra reward that each coalition has received up to the current time to re-adjust the allocations among the players. As main result, we provide a constructive method for designing allocation rules that converge to the core of the average game. Both the set up and the solution approach also provide an insight on commonalities between coalitional games and stability theory.
Constrained consensus for bargaining in dynamic coalitional TU games
2011
We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. We assume that the players in the game interact only with their neighbors, where the neighbors may vary over time. The main contributions of the paper are the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining protocol to a random allocation that lies in the core of the robust game under some mild conditions on the players' communication graphs.
Modular Strategies for Recursive Game Graphs
2006
AbstractMany problems in formal verification and program analysis can be formalized as computing winning strategies for two-player games on graphs. In this paper, we focus on solving games in recursive game graphs which can model the control flow in sequential programs with recursive procedure calls. While such games can be viewed as the pushdown games studied in the literature, the natural notion of winning in our framework requires the strategies to be modular with only local memory; that is, resolution of choices within a module does not depend on the context in which the module is invoked, but only on the history within the current invocation of the module. While reachability in (global…
Advantage of Quantum Strategies in Random Symmetric XOR Games
2013
Non-local games are known as a simple but useful model which is widely used for displaying nonlocal properties of quantum mechanics. In this paper we concentrate on a simple subset of non-local games: multiplayer XOR games with 1-bit inputs and 1-bit outputs which are symmetric w.r.t. permutations of players.
On symmetric nonlocal games
2013
Abstract Nonlocal games are used to display differences between the classical and quantum world. In this paper, we study symmetric XOR games, which form an important subset of nonlocal games. We give simple methods for calculating the classical and the quantum values for symmetric XOR games with one-bit input per player. We illustrate those methods with two examples. One example is an N -player game (due to Ardehali (1992) [3] ) that provides the maximum quantum-over-classical advantage. The second example comes from generalization of CHSH game by letting the referee to choose arbitrary symmetric distribution of players’ inputs.
On Applying Adaptive Data Structures to Multi-Player Game Playing
2013
In the field of game playing, the focus has been on two-player games, such as Chess and Go, rather than on multi-player games, with dominant multi-player techniques largely being an extension of two-player techniques to an \(N\)-player environment. To address the problem of multiple opponents, we propose the merging of two previously unrelated fields, namely those of multi-player game playing and Adaptive Data Structures (ADS). We present here a novel move-ordering heuristic for a dominant multi-player game playing algorithm, namely the Best-Reply Search (BRS). Our enhancement uses an ADS to rank the opponents in terms of their respective threat levels to the player modeled by the AI algori…
From Global Games to Re-contextualized Games: The Design Process of TekMyst
2011
Designing, developing and testing a game for a specific learning context and then achieving positive results, encourages one to deploy it in other environments. We know however that it is not always possible to successfully transfer artifacts from one learning context to the next. In this chapter we explore the principles to be considered when re-contextualizing a game. We base our analysis on the transfer of a Hypercontextualized Game SciMyst (which was designed and developed for the Joensuu Science Festival) into its re-contextualized version TekMyst (for the Helsinki Museum of Technology). Employing a qualitative approach we review the requirements and design decisions at the hand of fou…
Novel threat-based AI strategies that incorporate adaptive data structures for multi-player board games
2016
This paper considers the problem of designing novel techniques for multi-player game playing, in a range of board games and configurations. Compared to the well-known case of two-player game playing, multi-player game playing is a more complex problem with unique requirements. To address the unique challenges of this domain, we examine the potential of employing techniques inspired by Adaptive Data Structures (ADSs) to rank opponents based on their relative threats, and using this information to achieve gains in move ordering and tree pruning. We name our new technique the Threat-ADS heuristic. We examine the Threat-ADS’ performance within a range of game models, employing a number of diffe…
Dynamic Coalitional TU Games: Distributed Bargaining among Players' Neighbors
2013
We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The game differs from other ones in the literature on dynamic, stochastic or interval valued TU games as it combines dynamics of the game with an allocation protocol for the players that dynamically interact with each other. The protocol is an iterative and decentralized algorithm that offers a paradigmatic mathematical description of negotiation and bargaining processes. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protoc…