Participation and Interaction in Projects: A Game-Theoretic Analysis

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.