We analyze the core of a class of coalition formation game in which every player's payoff depends only on the members of her coalition. We first consider anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additional strong properties are imposed. We then introduce two top-coalition properties each of which guarantee the existence. We show that these properties are independent of the Scarf-balancedness condition. Finally we give several economic applications.

We study coalition formation as an ongoing, dynamic process, with payoffs generated as coalitions form, disintegrate, or regroup. A process of coalition formation (PCF) is an equilibrium if a coalitional move to some other state can be "justified" by the expectation of higher future value, compared to inaction. This future value, in turn, is endogenous: it depends on coalitional movements at each node. We study existence of equilibrium PCFs. We connect deterministic equilibrium PCFs with unique absorbing state to the core, and equilibrium PCFs with multiple absorbing states to the largest consistent set. In addition, we study cyclical as well as stochastic equilibrium PCFs.

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Geographical concentration of stores that sell similar commodities is pervasive. To analyze this phenomenon, this paper provides a simple two dimensional spatial competition model with consumer taste uncertainty. Given taste uncertainty, concentration of stores attracts more consumers since more variety means that a consumer has a higher chance of finding her favorite commodity (a market size effect). On the other hand, concentration of stores leads to fiercer price competition (a price cutting effect). The trade-off between these two effects is the focus of this paper. We provide a few sufficient conditions for the nonemptiness of equilibrium store location choices in pure strategies. We illustrate, by an example, that the market size effect is much stronger for small scale concentrations, but as the number of stores at the same location becomes larger, the price cutting effect eventually dominates. We also discuss consumers' incentives to visit a concentration of stores instead of using mail orders.

We study a generalization of Shapley-Scarf's (1974) economy in which multiple types of indivisible goods are traded. We show that many of the distinctive results from the Shapley-Scarf economy do not carry over to this model, even if agents' preferences are strict and can be represented by additively separable utility functions. The core may be empty. The strict core, if nonempty, may be multi-valued, and might not coincide with the set of competitive allocations. Furthermore, there is no Pareto efficient, individually rational, and strategy-proof social choice rule. We also show that the core may be empty in the class of economies with a single type of indivisible good and agents consuming multiple units, even if no complementarity exists among the goods.