The first chapter is based on a paper with Jingyi Xue in fair division problems. In this chapter, we consider the problem of fairly dividing a finite number of divisible goods among agents with the generalized Leontief preferences. We propose and characterize the class of generalized egalitarian rules which satisfy efficiency, group strategy-proofness, anonymity, resource monotonicity, population monotonicity, envy-freeness and consistency. On the Leontief domain, our rules generalize the egalitarian-equivalent rules with reference bundles. We also extend our rules to agent-specific and endowment-specific egalitarian rules. The former is a larger class of rules satisfying all the previous properties except anonymity and envy-freeness. The latter is a class of efficient, group strategy-proof, anonymous and individually rational rules when the resources are assumed to be privately owned.

The second chapter is about monopoly pricing with social learning. In this chapter, we consider a two-period monopolistic model in which the consumers who purchase in the first period would reveal the unknown quality of the product through their experiences to the consumers in the second period. Due to this effect, some consumers would strategically choose to delay to the second period in order to take this informational free-ride. We show that there always exists a unique symmetric equilibrium of consumers for each price set by the monopolist. Then we further investigate the seller’s optimization pricing problem. In a range of moderate patience, the seller would be likely to induce the consumers to effectively transmit information. We also discuss the impact of information disclosure on the monopolistic profit.