Asaf Plan

Interests

Research

Microeconomic theory, game theory, behavioral economics

Teaching

Game Theory, Behavioral Economics, Consumer Choice, Dynamic Economics Analysis

Courses

Scholarly Contributions

Journals/Publications

• Plan, A. (2017). Symmetric n-player games. Journal of Economic Theory.
• Plan, A. (2017). Symmetric n-player games. Theoretical Economics.
• Plan, A. (2023).

  Symmetry in n-player games

  . Journal of Economic Theory. doi:10.1016/j.jet.2022.105549
  More info

  This paper regards symmetry in games with more than two players. It is often said that a two-player game is symmetric if it looks the same to both players. However, there are n-player games, such as Salop's circle model, that seem intuitively to look the same to all players, but do not meet the common definition of a symmetric n-player game. This paper proposes a more general symmetry condition that is satisfied by such models. Previous authors have established that games which are symmetric in the common sense have a number of useful properties relating to equilibrium characterization and comparative statics. With few exceptions, those properties continue to hold in the richer class of games that meet the symmetry condition proposed here.
• Plan, A. (2010).

  Three Essays on Dynamic Games

  . dissertation.
  More info

  Chapter 1: This chapter considers a new class of dynamic, two-player games, where a stage game is continuously repeated but each player can only move at random times that she privately observes. A player's move is an adjustment of her action in the stage game, for example, a duopolist's change of price. Each move is perfectly observed by both players, but a foregone opportunity to move, like a choice to leave one's price unchanged, would not be directly observed by the other player. Some adjustments may be constrained in equilibrium by moral hazard, no matter how patient the players are. For example, a duopolist would not jump up to the monopoly price absent costly incentives. These incentives are provided by strategies that condition on the random waiting times between moves; punishing a player for moving slowly, lest she silently choose not to move. In contrast, if the players are patient enough to maintain the status quo, perhaps the monopoly price, then doing so does not require costly incentives. Deviation from the status quo would be perfectly observed, so punishment need not occur on the equilibrium path. Similarly, moves like jointly optimal price reductions do not require costly incentives. Again, the tempting deviation, to a larger price reduction, would be perfectly observed. This chapter provides a recursive framework for analyzing these games following Abreu, Pearce, and Stacchetti (1990) and the continuous time adaptation of Sannikov (2007). For a class of stage games with monotone public spillovers, like differentiated-product duopoly, I prove that optimal equilibria have three features corresponding to the discussion above: beginning at a low position, optimal, upward moves are impeded by moral hazard; beginning at a high position, optimal, downward moves are unimpeded by moral hazard; beginning at an intermediate position, optimally maintaining the status quo is similarly unimpeded. Corresponding cooperative dynamics are suggested in the older, non-game-theoretic literature on tacit collusion.Chapter 2: This chapter shows that in finite-horizon games of a certain class, small perturbations of the overall payoff function may yield large changes to unique equilibrium payoffs in periods far from the last. Such perturbations may tie together cooperation across periods in equilibrium, allowing substantial cooperation to accumulate in periods far from the last.Chapter 3: A dynamic choice problem faced by a time-inconsistent individual is typically modeled as a game played by a sequence of her temporal selves, solved by SPNE. It is recognized that this approach yields troublesomely many solutions for infinite-horizon problems, which is often attributed to the existence of implausible equilibria based on self-reward and punishment. This chapter presents a refinement applicable within the special class of strategically constant (SC) problems, which are those where all continuation problems are isomorphic. The refinement requires that each self's strategy be invariant, here that implies history-independence under the isomorphism. I argue that within the class of SC problems, this refinement does little more than rule out self-reward and punishment. The refinement substantially narrows down the set of equilibria in SC problems, but in some cases allows plausible equilibria that are excluded by other refinement approaches. The SC class is limited, but broader than it might seem at first.

Presentations

• Plan, A. (2016, April). The finite-horizon paradox with impatient players. Theory seminar at UT Austin.
• Plan, A. (2016, March). The competitive effects of an improvement in the accuracy of consumers' product comparisons. Southwestern Economic Theory Conference. UC Riverside.
• Plan, A. (2016, Summer). The finite-horizon paradox with impatient players. Games 2016, the 5th world congress of the Game Theory Society. Maastricht: Game Theory Society.
• Plan, A. (2014, Fall). The competitive effects of an improvement in the accuracy of consumers' product comparisons. Theory seminar. Arizona State University.