Throughout the thesis, I study mathematical models that can help explain the dependency of social phenomena in animals and humans on individual traits. The first chapter investigates consensus building in human groups through communication of individual preferences for a course of action. Individuals share and modify these preferences through speaker listener interactions. Personality traits, reputations, and social networks structures effect these modifications and eventually the group will reach a consensus. If there is variation in personality traits, the time to reach consensus is delayed. Reputation models are introduced and explored, finding that those who can best estimate the average initial preference and who have the best knowledge to what the optimal decision is for the group become the most reputable. If there is one individual, an informal leader, who is stubborn, persuasive, reputable, and socially connected then the time to reach consensus is reduced. The second chapter introduces a model for the emergence of play behavior in animals. An individual-based model is proposed where organisms compete for resources in the environment. Play is introduced as a frivolous behavior that increases energy use and the probability of dying. Simulations show that play behavior becomes fixed in the population and the time spent playing is maintained at a low rate in regardless of its costly nature. When play behavior is directly functional by increasing foraging ability, it evolves quickly and the time individuals spend playing increases, but eventually the population of players collapses and play disappears. Play acts as a spiteful behavior in that playing individuals suffer a direct cost to their fitness, but also results in players consuming more resources incurring a greater cost to other individuals in the population through reduced probability of successfully foraging
