Cooperation under Imperfect Monitoring and External Threat

Cooperation among players is often a good deed to pursue. The famous "Prisoner’s Dilemma" in game theory has long been an example of showing how non-cooperation results because of conflict of interest among agents. My thesis investigates how factors like imperfect public monitoring, emergence of an external threat influences the cooperative behaviors among players in dynamic environments. Chapter 1 investigates bidder collusion in repeated procurement auctions without communication or side payments, focusing on the case of bidders having identical costs under imperfect public monitoring where only winners, not bids, are publicly observed. It presents a simple bid rotation scheme, in which bidders take turns entering bids equal to the auction’s reserve price. This behavior is supported by the threat of a bidding war, i.e. if an auction is won by the wrong bidder, all bidders will enter bids equal to their common production cost in all future auctions. Bid rotation maximizes the bidders’ joint profits and is a perfect public equilibrium if and only if the discount factor is greater than or equal to a critical value, call it delta. This paper presents two main results. First, except for a measure zero set of discount factors, joint profit maximization cannot be achieved for discount factors below delta by any profile of bidding strategies. Second, in the case of two bidders, there is no profile of bidding strategies that achieves joint profit maximization for discount factors less than or equal to delta. Chapter 2 investigates a situation where firms selling different products refer mis- allocated customers to one another. Under monitoring over each other’s sales in every period, we analyze firm referrals in an infinitely repeated game with by looking at a class of “k + 1 punishment schemes”, in which players “forgive” the first k bad signals, and “punish” each other forever after the k + 1’s bad signal. We characterize the unique optimal k in this class of schemes. Chapter 3 is an empirical paper that models the impacts of telemarketing calls for selling bank long-term deposits. We use a dataset from a Portuguese retail bank from 2008 to 2013. This dataset contains features related to the calls and customers. We model a binary response of the outcome of the telemarketing call (yes or no) using those features. In second part of the paper, we propose methods to model price elasticity of demand (PED), which measures sensitivity of the long-term deposits resulting from changing interest rates. In estimating the PEDs, propensity-score-matching is used to adjust for potential group differentiation. Chapter 4 studies alliance behavior under external threat. When an alliance faces danger of appropriation from an external enemy, it is optimum for its members to jointly invest in their defense. For members to behave collusively in the subgame perfect Nash equilibrium (SPNE), each of them has to be allocated with some minimum share of that resource. Under proportion-to-share rule of cost contribution and profit earning, this paper looks at how that minimum share requirement changes after the emergence of the external threat. We find that two factors, alliance size and cost factor contribute to the stability of the alliance in opposite directions. Further, force from more costly investment outweighs the force from increasing alliance size, which makes the alliance easier to maintain