XI. Winter Workshop in Economics

Friday, December 29, 2017

Koç University

Micro/Theory Session - Abstracts


Investments in Bargaining Positions: Proposer-optimal Mechanisms


Kemal Kıvanç Aköz

New York University Abu Dhabi (with N. Anbarcı)


Abstract

In this paper, we consider a bargaining setup where investments by a party can only improve one's bargaining position without improving the surplus. At any point in the game, Player 1 can make Player 2 an offer, who can have one of the two possible levels of initial bargaining position, namely high and low, and can also make an investment in her initial bargaining position. The total of Player 2’s initial bargaining position and her investment will constitute her final bargaining position. In the complete-information case, the final bargaining position of Player 2 is fully observable by Player 1. Player 1 can either wait for Player 2 to make her optimal investment and then match any outside offer by a counter offer by the market or can instead make a pre-emptive offer before Player 2 can make any investment. It turns out that a pre-emptive offer is fully efficient and the counter-offer is not; the payoff difference between them is fully channelled to Player 1. In the no information case, neither the initial bargaining position nor her investment is observable by Player 1 at all. In that case, when Player 1’s prior belief about the high type of Player 2 is high, then Player 1 chooses to make an offer that both types of Player 2 accept. It is fully efficient but the low type of Player 2 gains and Player 1 loses from that offer relative to the complete-information outcome. When Player 1’s prior belief about the high type of Player 2 is not very high, then Player 1 chooses to make a counter offer, in which case the outcome clearly is not efficient. In the noisy-information case, Player 1 can receive two separate signals. One signal is about Player 2’s initial bargaining position, which will be zero when 2’s investment level is zero and non-zero otherwise. The other signal is about Player 2’s investment level. When the cumulative signal is high, just like in the no-information case, Player 1 makes an offer that both types of Player 2 accept. When Player 1’s prior belief about the high type of Player 2 is not very high, then Player 1 chooses to make a counter offer if and only if Player 2 gets an offer without any investment activity, in which case the outcome clearly is efficient and equivalent to the one in the complete-information case.

Multilateral Limit Pricing in Price-Setting Games


Eray Cumbul

TOBB-ETU University (with G. Virag)


Abstract

In this paper, we characterize the set of pure strategy equilibria in differentiated Bertrand oligopolies with linear demand and constant unit costs when firms may prefer not to produce. When there are two firms or all firms are active, there is a unique equilibrium. However, there is a continuum of Bertrand equilibria on a wide range of parameter values when the number of firms (n) is more than two and n* is in [2,n-1] firms are active.In each such equilibrium, the relatively more cost or quality efficient firms limit their prices to induce the exit of their rival(s). When n >= 3, this game do not need to satisfy supermodularity, the single-crossing property (SCP), or log-supermodularity (LS). Moreover, best responses might have negative slopes. These results are very di_erent from those in the existing literature on Bertrand models with differentiated products, where uniqueness, supermodularity, the SCP, and LS usually hold under a linear market demand assumption, and best response functions slope upward. Our main results extend to a Stackelberg entry game where some established incumbents first set their prices and then a potential entrant sets its price.

Intransitive Indifference Under Uncertainty: Expected Scott-Suppes Utility Representation


Nuh Aygün Dalkıran

Bilkent University (with O. Dokumacı and T. Kara)


Abstract

We study preferences with intransitive indifference under uncertainty. Our primitives are semiorders and we are interested in their Scott-Suppes representations. We obtain a Scott-Suppes representation theorem in the spirit of the expected utility theorem of von Neumann and Morgenstern (1944). Our representation offers a decision theoretical interpretation for epsilon equilibrium.

Moral Hazard, Uncertain Technologies, and Linear Contracts


Martin Dumay

Universidad Carlos III de Madrid (with U. Khan)


Abstract

We analyze a moral hazard problem where both contracting parties face nonprobabilistic uncertainty about how actions translate to output and seek robust performance from a contract in relation to their respective worst-case scenarios. Linear contracts that align Principal's and Agent's pessimistic expectations are optimal.

Bargaining with Periodic Participation Costs


Emin Karagözoğlu

Bilkent University (with S. Rachmilevitch)


Abstract

We study a bargaining game in which a player needs to pay a fixed cost in the beginning of every period t, if he wants to stay in the game in period t+1, in case a deal has not been reached by the end of t. Whether a player pays this cost is his private information. Every efficient payoff vector can be approximated in equilibrium. When costs of delay vanish, the value of every symmetric stationary equilibrium converges to zero. Applications of our model include bargaining through representatives, trading off bargaining and other activities, and collusion in auctions.

Sabotage in Team Contests


Kerim Keskin

Kadir Has University (with S. Doğan and Ç. Sağlam)


Abstract

In the contest literature, sabotage is de ned as a deliberate and costly activity which damages the opponent's likelihood of winning the contest. The existing results mostly suggest that contestants are discouraged anticipating a possible sabotage. In this paper we investigate the act of sabotage in a team contest where team members exert costly effort as a contribution to their team's aggregate effort which in turn determines the contest outcome. For the baseline model with no sabotage, there exists a corner equilibrium indicating a free-rider problem in each team. As for the model with sabotage, our characterization of Nash equilibrium reveals two important results: (i) There exists a unique interior equilibrium so that the free-rider problem is nolonger a concern; and (ii) The discouragement effect of sabotage vanishes for some players. Furthermore, we investigate the team owner's problems of prize allocation and team formation considering the objective to maximize his team's winning probability.