Decision theory: von Neumann's contributions.
Degrees of indeterminacy of games
Delegation equilibrium payoffs in integer-splitting games
This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their payoffs in...
Design of a Participatory Decision Making Agent Architecture Based on Argumentation and Influence Function – Application to a Serious Game about Biodiversity Conservation
This paper addresses an ongoing experience in the design of an artificial agent taking decisions and combining them with the decisions taken by human agents. The context is a serious game research project, aimed at computer-based support for participatory management of protected areas (and more specifically national parks) in order to promote biodiversity conservation and social inclusion. Its objective is to help various stakeholders (e.g., environmentalist, tourism operator) to collectively understand...
Détermination des jeux boréliens et problèmes logiques associés
Deterministic Markov Nash equilibria for potential discrete-time stochastic games
In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games and the stochastic...
Diagonal checker-jumping and Eulerian numbers for color-signed permutations.
Diagonal peg solitaire.
Differential Games and Nonlinear First Order PDE on Bounded Domains.
Discrepancy games.
Discrete and nondiscrete duels
Discrete bidding games.
Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous approaches...
Discretized feedback for differential games
Disjointness of fuzzy coalitions
The cooperative games with fuzzy coalitions in which some players act in a coalition only with a fraction of their total “power” (endeavor, investments, material, etc.) or in which they can distribute their “power” in more coalitions, are connected with some formal or interpretational problems. Some of these problems can be avoided if we interpret each fuzzy coalition as a fuzzy class of crisp coalitions, as shown by Mareš and Vlach in [9,10,11]. The relation between this model of fuzziness and...
Division schemes under uncertainty of claims
In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with...
Domination Game: Extremal Families for the 3/5-Conjecture for Forests
In the domination game on a graph G, the players Dominator and Staller alternately select vertices of G. Each vertex chosen must strictly increase the number of vertices dominated. This process eventually produces a dominating set of G; Dominator aims to minimize the size of this set, while Staller aims to maximize it. The size of the dominating set produced under optimal play is the game domination number of G, denoted by γg(G). Kinnersley, West and Zamani [SIAM J. Discrete Math. 27 (2013) 2090-2107]...
Duels with possibly asymmetric goals
Dynamic one-pile blocking Nim.
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...