The Formation of Rank Structure Through Self Interested Interactions

I study the process of coalition formation when competing agents benefit by cooperating with each other out of self-interest. The payoff to agents depends on their relative skill (rank). Agents benefit from mutual interactions - where agreements are non-binding - that leads to the formation of coalitions. Assuming complete information, I develop an algorithm that segregates agents into coalitions depending on the strategies they play. I prove that a Coalitional Equilibrium does not necessarily exist in this economy. For the case of 2-Rank Stable Economy: an economy where no agent's rank can increase by two or more ranks, I show that the rank ordering will not change due to mutual interactions; it will be identical to the initial rank ordering. For the general case of m-Rank Stable Economy, where rank ordering could change, I establish the necessary and sufficient conditions for agents to increase their ranks