4 Presentations

• 
  10:40 AM - 11:05 AM

  Cournot duopolies with uncertainty in the production costs

  • Bruno M. P. M. Oliveira, presenter, FCNAUP and INESC TEC
  • Joana Becker Paulo, FCUP
  • Alberto Pinto, University of Porto

  We consider an economic model of two firms in Cournot competition in a two stages game. In the first stage, firms have an initial (high) cost and may choose to invest to have the chance of obtaining a lower cost. The low cost is given by the Ferreira-Oliveira-Pinto R&D investment function. After choosing their investment, firms know the outcome of their R&D program, i.e. if their cost will be high or low. However, each firm will be uncertain of the production cost of their rival, knowing only the probability of their production cost being high or low. On the second stage, firms will have to choose the quantity. This game can be divided in six distinct types of economic cases, depending of the production costs. We obtained explicit expressions for the optimal quantity output for each firm, i.e. the Nash equilibria for the quantity game. Furthermore, we present explicit formulas for the prices and the profits. Regarding the investment game, the first stage game, we present the candidates for the optimal investment in the reduction of the production costs, that are the zeros of a third order polynomial, with coefficients that depend on the economic case.

• 
  11:05 AM - 11:30 AM

  Welfare Comparison of School Choice Mechanisms under Incomplete Information

  • Ethem Akyol, presenter, TOBB University of Economics and Technology

  We compare two widely used allocation methods for school choice, the Deferred Acceptance (DA) mechanism and the Boston mechanism, in terms of welfare. We consider a symmetric incomplete information setting in which students have independently drawn (cardinal) valuations for schools and all schools have an identical ranking of the students. Our main result is that when each school has one available seat and the number of schools and students is large, every type of every student has a higher interim utility under the Boston mechanism than under the DA mechanism. Although this strong result is not true when the number of schools is small, even in this case, the Boston mechanism is ex-ante welfare superior to DA under weak conditions on the distribution of valuations.

• 
  11:30 AM - 11:55 AM

  Prize formation and sharing in dynamic contests

  • Vladimir Petkov, presenter, Victoria University of Wellington

  This paper examines a dynamic contest between two players. In each period, their effort may contribute to a joint prize pool, while also generating private costs. The player who works harder is awarded a larger share of the current prize pool, but his opponent also receives a positive (albeit smaller) share. The stages of the dynamic contest are linked through delayed effects of effort on the subsequent prize pools. Thus, our setting exhibits both static and intertemporal rank-order spillovers. Under specific assumptions, this game may have an equilibrium in which the players use state-contingent mixed strategies with continuous support. The state dynamics and the prize pool are assumed to have a piecewise linear structure, implying expected lifetime payoffs that are linear in the state variable. We characterize the equilibrium mixing distribution, expected effort levels and payoffs. Then we illustrate them with several examples.

• 
  11:55 AM - 12:20 PM

  Optimal price equilibrium under social differentiation

  • Alberto Pinto, presenter, University of Porto

  We study a usual duopoly game with a two-stage game. In the first stage firms choose their prices and in the second stage individuals choose in which firm they are going to buy. The inicial setup is the Bertrand price model. We add a new term to the utilities of the individuals: the social influence in choices. We are able to fully characterise the local perfect equilibria: some individuals decide to be loyal to some firm and others choose a mix strategy. Our new model brings a new understanding of the Bertrand paradox.