Mechanism Design for Team Formation

Team formation is a core problem in AI. Remarkably, little prior work has addressed the problem of mechanism design for team formation, accounting for the need to elicit agents' preferences over potential teammates. Coalition formation in the related hedonic games has received much attention, but only from the perspective of coalition stability, with little emphasis on the mechanism design objectives of true preference elicitation, social welfare, and equity. We present the first formal mechanism design framework for team formation, building on recent combinatorial matching market design literature. We exhibit four mechanisms for this problem, two novel, two simple extensions of known mechanisms from other domains. Two of these (one new, one known) have desirable theoretical properties. However, we use extensive experiments to show our second novel mechanism, despite having no theoretical guarantees, empirically achieves good incentive compatibility, welfare, and fairness.Comment: 12 page

Optimal Partitions in Additively Separable Hedonic Games

We conduct a computational analysis of fair and optimal partitions in additively separable hedonic games. We show that, for strict preferences, a Pareto optimal partition can be found in polynomial time while verifying whether a given partition is Pareto optimal is coNP-complete, even when preferences are symmetric and strict. Moreover, computing a partition with maximum egalitarian or utilitarian social welfare or one which is both Pareto optimal and individually rational is NP-hard. We also prove that checking whether there exists a partition which is both Pareto optimal and envy-free is $\Sigma_{2}^{p}$-complete. Even though an envy-free partition and a Nash stable partition are both guaranteed to exist for symmetric preferences, checking whether there exists a partition which is both envy-free and Nash stable is NP-complete.Comment: 11 pages; A preliminary version of this work was invited for presentation in the session `Cooperative Games and Combinatorial Optimization' at the 24th European Conference on Operational Research (EURO 2010) in Lisbo

Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2

The Behavioral Impact of Emotions in a Power-to-Take Game: An Experimental Study

The power-to-take game is a simple two player game where players are randomly divided into pairs consisting of a take authority and responder. Both players in each pair have earned an income in an individual real effort decision-making experiment preceding the take game. The game consists of two stages. In the first stage, the take authority decides how much of the earned income of the responder that is left after the second stage will be transferred to the take authority (the so-called take rate). In the second stage, the responder can punish the take authority by destroying (part of) his or her earned income. In this experimental study, we are primarily interested in how emotions influence responder behavior. Our findings are the following. (1) A higher take rate significantly increases the intensity of irritation, contempt, and envy, and significantly decreases the intensity of joy and happiness. Since negative emotions are experienced as painful, there is direct hedonic impact. (2) Irritation and contempt drive punishment behavior. (3) There are discontinuous "jumps" in the behavior of responders. They either choose no punishment (destroy nothing) or the highest level of punishment (destroy everything). (4) Expectations have a significant effect on the probability of punishment but not on the intensity of experienced emotion. This last result is explained in terms of norm-related regulation of emotions.Emotions, punishment, expectations, social norms, experiment

Hedonic Seat Arrangement Problems

In this paper, we study a variant of hedonic games, called \textsc{Seat Arrangement}. The model is defined by a bijection from agents with preferences to vertices in a graph. The utility of an agent depends on the neighbors assigned in the graph. More precisely, it is the sum over all neighbors of the preferences that the agent has towards the agent assigned to the neighbor. We first consider the price of stability and fairness for different classes of preferences. In particular, we show that there is an instance such that the price of fairness ({\sf PoF}) is unbounded in general. Moreover, we show an upper bound $\tilde{d}(G)$ and an almost tight lower bound $\tilde{d}(G)-1/4$ of {\sf PoF}, where $\tilde{d}(G)$ is the average degree of an input graph. Then we investigate the computational complexity of problems to find certain ``good'' seat arrangements, say \textsc{Maximum Welfare Arrangement}, \textsc{Maximin Utility Arrangement}, \textsc{Stable Arrangement}, and \textsc{Envy-free Arrangement}. We give dichotomies of computational complexity of four \textsc{Seat Arrangement} problems from the perspective of the maximum order of connected components in an input graph. For the parameterized complexity, \textsc{Maximum Welfare Arrangement} can be solved in time $n^{O(\gamma)}$, while it cannot be solved in time $f(\gamma)^{o(\gamma)}$ under ETH, where $\gamma$ is the vertex cover number of an input graph. Moreover, we show that \textsc{Maximin Utility Arrangement} and \textsc{Envy-free Arrangement} are weakly NP-hard even on graphs of bounded vertex cover number. Finally, we prove that determining whether a stable arrangement can be obtained from a given arrangement by $k$ swaps is W[1]-hard when parameterized by $k+\gamma$, whereas it can be solved in time $n^{O(k)}$

Economic Games Quantify Diminished Sense of Guilt in Patients with Damage to the Prefrontal Cortex

Damage to the ventromedial prefrontal cortex (VMPFC) impairs concern for other people, as reflected in the dysfunctional real-life social behavior of patients with such damage, as well as their abnormal performances on tasks ranging from moral judgment to economic games. Despite these convergent data, we lack a formal model of how, and to what degree, VMPFC lesions affect an individual's social decision-making. Here we provide a quantification of these effects using a formal economic model of choice that incorporates terms for the disutility of unequal payoffs, with parameters that index behaviors normally evoked by guilt and envy. Six patients with focal VMPFC lesions participated in a battery of economic games that measured concern about payoffs to themselves and to others: dictator, ultimatum, and trust games. We analyzed each task individually, but also derived estimates of the guilt and envy parameters from aggregate behavior across all of the tasks. Compared with control subjects, the patients donated significantly less and were less trustworthy, and overall our model found a significant insensitivity to guilt. Despite these abnormalities, the patients had normal expectations about what other people would do, and they also did not simply generate behavior that was more noisy. Instead, the findings argue for a specific insensitivity to guilt, an abnormality that we suggest characterizes a key contribution made by the VMPFC to social behavior

The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories

This paper surveys recent experimental and field evidence on the impact of concerns for fairness, reciprocity and altruism on economic decision making. It also reviews some new theoretical attempts to model the observed behavior.Behavioural Economics; Other-regarding Preferences; Fairness; Reciprocity; Altruism; Experiments; Incentives; Contracts; Competition

The Economics of Fairness, Reciprocity and Altruism – Experimental Evidence and New Theories

Chapter written for the Handbook of Reciprocity, Gift-Giving and AltruismBehavioural Economics; Other-regarding Preferences; Fairness; Reciprocity; Altruism; Experiments; Incentives; Contracts; Competition

Advances in Negotiation Theory: Bargaining, Coalitions and Fairness

Bargaining is ubiquitous in real-life. It is a major dimension of political and business activities. It appears at the international level, when governments negotiate on matters ranging from economic issues (such as the removal of trade barriers), to global security (such as fighting against terrorism) to environmental and related issues (e.g. climate change control). What factors determine the outcome of negotiations such as those mentioned above? What strategies can help reach an agreement? How should the parties involved divide the gains from cooperation? With whom will one make alliances? This paper addresses these questions by focusing on a non-cooperative approach to negotiations, which is particularly relevant for the study of international negotiations. By reviewing non-cooperative bargaining theory, non-cooperative coalition theory, and the theory of fair division, this paper will try to identify the connection among these different facets of the same problem in an attempt to facilitate the progress towards a unified framework.Negotiation theory, Bargaining, Coalitions, Fairness, Agreements