Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1609.01921

A Model for Partial Kantian Cooperation

Ioannis Kordonis
View original source ↗Read source document ↗Export metadata ↓

Abstract

In several game situations, the behavior of the players may depend not only on individual interests, but also on what each player considers as the correct thing to do. This work presents a game theoretic model, aiming to describe game situations in which the players' behavior is affected by ethical considerations. Particularly, we assume that they partially follow, Kant's `Categorical Imperative'. The model is stated for games with a continuum of players. The basic assumption made is that the participants perceive that they belong to virtual (imagined) groups, in which they optimize their actions as if they were bound to follow the same strategy. A partially cooperative equilibrium, called $r$-Kant-Nash equilibrium is then introduced. We then study the relationship of the $r$-Kant-Nash equilibrium with the Nash, (Bentham-) Harsanyi, Rawls difference and Roemer solutions. For the case where the set of possible player types is finite, we prove sufficient conditions for the existence and uniqueness of the $r$-Kant-Nash equilibrium and the equilibrium is characterized in terms of a variational inequality. For the case of continuous types, necessary conditions characterizing the partial Kantian equilibria are derived using a reduction to a set of optimal control problems. Finally, some numerical examples are given.

Explore related subjects

cs.GT

Keep this discovery

BibTeXRIS

Ioannis Kordonis. 2016-09-07. A Model for Partial Kantian Cooperation. https://arxiv.org/abs/1609.01921

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

MMS Allocation for Chores with Online Agent Arrivals

We study the fair allocation of $m$ indivisible chores to $n$ agents with subadditive cost functions arriving online in an arbitrary order. Upon an agent's arrival, we are informed of her cost function and must irrevocably assign her a set of chores. We focus on the Maximin Share (MMS) fairness notion and aim to compute an allocation in which all items are assigned, and no agent incurs a cost more than $\alpha$ times her MMS. Without any prior information about the instance (other than $n$ and $m$), we design an algorithm with a competitive ratio of $O(\min\{n, k\log^{1+\epsilon}k, \log m\})$ for any constant $\epsilon > 0$, where $k$ denotes the number of cost function types. Our bound matches the best known offline approximation guarantees for MMS under subadditive costs and is nearly optimal with respect to all three parameters: we show that even for binary additive cost functions, no online algorithm can achieve a competitive ratio of $o(\min\{n, k\log k, \log m\})$. We then consider the setting in which the $k$ cost function types are known in advance (though the realized types of arriving agents are not). For additive cost functions, we provide an algorithm with a competitive ratio of $O(\min\{\log k, \log(kn)/\log\log(kn)\})$, and show that constant-competitive algorithms do not exist for general $k$, even for the binary additive setting. For binary additive functions when $k \le n$, we propose a $3$-competitive algorithm and establish a lower bound of $2$.

cs.GT↗
arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗
arXiv2026

Existence of the Core in Approval-Based Committee Elections

We settle the main open question in the theory of approval-based multi-winner elections: we show that there always exists a committee in the core. The core is a stability and group fairness concept. The proof introduces a new voting rule that optimizes an entropy-like objective function over committees and payment systems. All local optima of this objective function lie in the core, which implies that a core committee can be found in polynomial time.

cs.GT↗