Consider people dividing their time and effort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on efficient effort division, we determine the existence and efficiency of the Nash equilibria of the game of allocating effort to such projects. When no minimum effort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal effort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.

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A paper needs to be good enough to be published; a grant proposal needs to be sufficiently convincing compared to the other proposals, in order to get funded. Papers and proposals are examples of cooperative projects that compete with each other and require effort from the involved agents, while often these agents need to divide their efforts across several such projects. We aim to provide advice how an agent can act optimally and how the designer of such a competition (e.g., the program chairs) can create the conditions under which a socially optimal outcome can be obtained. We therefore extend a model for dividing effort across projects with two types of competition: a quota or a success threshold. In the quota competition type, only a given number of the best projects survive, while in the second competition type, only the projects that are better than a predefined success threshold survive. For these two types of games we prove conditions for equilibrium existence and efficiency. Additionally we find that competitions using a success threshold can more often have an efficient equilibrium than those using a quota. We also show that often a socially optimal Nash equilibrium exists, but there exist inefficient equilibria as well, requiring regulation.

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Consider people dividing their time and eort between friends, interest clubs, and reading seminars. These are all reciprocal interactions, and the reciprocal processes determine the utilities of the agents from these interactions. To advise on ecient eort division, we determine the existence and eciency of the Nash equilibria of the game of allocating eort to such projects. When no minimum eort is required to receive reciprocation, an equilibrium always exists, and if acting is either easy to everyone, or hard to everyone, then every equilibrium is socially optimal. If a minimal eort is needed to participate, we prove that not contributing at all is an equilibrium, and for two agents, also a socially optimal equilibrium can be found. Next, we extend the model, assuming that the need to react requires more than the agents can contribute to acting, rendering the reciprocation imperfect. We prove that even then, each interaction converges and the corresponding game has an equilibrium.@en

A paper needs to be good enough to be published; a grant proposal needs to be suciently convincing compared to the other proposals, in order to get funded. Papers and proposals are examples of cooperative projects that compete with each other and require eort from the involved agents, while often these agents need to divide their eorts across several such projects. We aim to provide advice how an agent can act optimally and how the designer of such a competition (e.g., the program chairs) can create the conditions under which a socially optimal outcome can be obtained. We therefore extend a model for dividing eort across projects with two types of competition: a quota or a suc-cess threshold. In the quota competition type, only a given number of the best projects survive, while in the second competition type, only the projects that are better than a predened success threshold survive. For these two types of games we prove conditions for equilibrium existence and eciency. Additionally we nd that competitions using a success threshold can more often have an ecient equilibrium than those using a quota. We also show that often a socially optimal Nash equilibrium exists, but there exist inecient equilibria as well, requiring regulation@en

People often have reciprocal habits, almost auto- matically responding to others’ actions. A robot who interacts with humans may also reciprocate, in order to come across natural and be predictable. We aim to facilitate decision sup- port that advises on utility-efficient habits in these interac- tions. To this end, given a model for reciprocation behavior with parameters that represent habits, we define a game that describes what habit one should adopt to increase the utility of the process. This paper concentrates on two agents. The used model defines that an agent’s action is a weighted com- bination of the other’s previous actions (reacting) and either i) her innate kindness, or ii) her own previous action (inertia). In order to analyze what happens when everyone reciprocates rationally, we define a game where an agent may choose her habit, which is either her reciprocation attitude (i or ii), or both her reciprocation attitude and weight. We characterize the Nash equilibria of these games and consider their effi- ciency. We find that the less kind agents should adjust to the kinder agents to improve both their own utility as well as the social welfare. This constitutes advice on improving coopera- tion and explains real life phenomena in human interaction, such as the societal benefits from adopting the behavior of the kindest person, or becoming more polite as one grows up.@en

Much of what agents (people, robots, etc.) do is dividing effort between several activities. In order to facilitate efficient divisions, we study contributions to such activities and advise on stable divisions that result in high social welfare. To this end, for each model (game), we find the Nash equilibria and their social welfare. A Nash equilibrium is division where no agent can increase her utility if the others do not change their behavior. The social welfare is defined as the sum of the utilities of all the agents. We concentrate on value-creating activities and on reciprocation (interactions where agents react on the previous actions). The value-creating activities model work projects, co-authoring articles, writing to Wikipedia, etc. We assume that all the agents who contribute to such an activity at least a predefined threshold share of the final value of the activity. Examples of reciprocation activities are politics and relationships with colleagues. We prove the actions stabilize around a limit value. Then, we assume that agents strategically set their own interaction habits and model this as a game. We finally analyze dividing own effort between several reciprocal interactions. We lay the foundation of realistic mathematical modeling and analysis of effort division between activities and provide advice about what the agents should do in order to maximize the personal and the social welfare. @en

People often interact repeatedly: with relatives, through file sharing, in politics, etc. Many such interactions are reciprocal: reacting to the actions of the other. In order to facilitate decisions regarding reciprocal interactions, we analyze the development of reciprocation over time. To this end, we propose a model for such interactions that is simple enough to enable formal analysis, but is sufficient to predict how such interactions will evolve. Inspired by existing models of international interactions and arguments between spouses, we suggest a model with two reciprocating attitudes where an agent's action is a weighted combination of the others' last actions (reacting) and either i) her innate kindness, or ii) her own last action (inertia). We analyze a network of repeatedly interacting agents, each having one of these attitudes, and prove that their actions converge to specific limits. Convergence means that the interaction stabilizes, and the limits indicate the behavior after the stabilization. For two agents, we describe the interaction process and find the limit values. For a general connected network, we find these limit values if all the agents employ the second attitude, and show that the agents' actions then all become equal. In the other cases, we study the limit values using simulations. We discuss how these results predict the development of the interaction and constitute the first step towards helping agents decide on their behavior.@en

We consider an environment where sellers compete over buyers. All sellers are a-priori identical and strategically signal buyers about the product they sell. In a setting motivated by online advertising in display ad exchanges, where firms use second price auctions, a firm’s strategy is a decision about its signaling scheme for a stream of goods (e.g., user impressions), and a buyer’s strategy is a selection among the firms. In this setting, a single seller will typically provide partial information, and consequently, a product may be allocated inefficiently. Intuitively, competition among sellers may induce sellers to provide more information in order to attract buyers and thus increase efficiency. Surprisingly, we show that such a competition among firms may yield significant loss in consumers’ social welfare with respect to the monopolistic setting. Although we also show that in some cases, the competitive setting yields gain in social welfare, we provide a tight bound on that gain, which is shown to be small with respect to the preceding possible loss. Our model is tightly connected with the literature on bundling in auctions.@en

Shared effort games model people’s contribution to projects and sharing the obtained profits. Those games generalize both public projects like writing for Wikipedia, where everybody shares the resulting benefits, and all-pay auctions such as contests and political campaigns, where only the winner obtains a profit. In θ-equal sharing (effort) games, a threshold for effort defines which contributors win and then receive their (equal) share. (For public projects θ = 0 and for all-pay auctions θ = 1.) Thresholds between 0 and 1 can model games such as paper co-authorship and shared homework assignments. We study existence and efficiency of such games, to know what will happen in a given situation and where an intervention may be needed to improve the social welfare. First, we fully characterize the conditions for the existence of a pure-strategy Nash equilibrium for two-player shared effort games with close budgets and project value functions that are linear on the received contribution and prove some efficiency results. Second, since the theory does not work for more players, fictitious play simulations are used to show when such an equilibrium exists and what its efficiency is. The results about existence and efficiency of these equilibria provide the likely strategy profiles and the socially preferred strategies to use in real life situations of contribution to public projects.@en

Shared effort games model people's contribution to projects and sharing the obtained profits. Those games generalize both public projects like writing for Wikipedia, where everybody shares the resulting benefits, and all-pay auctions such as contests and political campaigns, where only the winner obtains a profit. In $ heta$-equal sharing (effort) games, a threshold for effort defines which contributors win and then receive their (equal) share. (For public projects $ heta = 0$ and for all-pay auctions $ heta = 1$.) Thresholds between 0 and 1 can model games such as paper co-authorship and shared homework assignments. First, we fully characterize the conditions for the existence of a pure-strategy Nash equilibrium for two-player shared effort games with close budgets and project value functions that are linear on the received contribution and prove some efficiency results. Second, since the theory does not work for more players, fictitious play simulations are used to show when such an equilibrium exists and what its efficiency is. The results about existence and efficiency of these equilibria provide the likely strategy profiles and the socially preferred strategies to use in real life situations of contribution to public projects. @en

We consider game theoretic aspects of crowdsensing projects. Com-
mencing by studying putting effort in and sharing rewards from public
projects, we continue to emotion-influenced interrelations in human soci-
ety, including negotiations as a kind of such influence. These topics are
also highly relevant to many applications apart from crowdsensing.@en