620 research outputs found
Gambling in Contests
This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian Motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Contrary to the explicit cost for a higher stopping time in a war of attrition, here, higher stopping times are riskier, because players can go bankrupt. We derive a closed-form solution of the unique Nash equilibrium outcome of the game. In equilibrium, the trade-off between risk and reward causes a non-monotonicity: highest expected losses occur if the process decreases only slightly in expectation
Sequential Bargaining in a Stochastic Environment
This paper investigates the uniqueness of subgame perfect (SP) payoffs in a sequential bargaining game. Players are completely informed and the surplus to be allocated follows a geometric Brownian motion. This bargaining problem has not been analysed exhaustively in a stochastic environment. The aim of this paper is to provide a technique to identify the subgame perfect equilibria, i.e. the timing of the agreement and the SP payoffs at which agreement occurs. Even though the main focus is on the uniqueness of the equilibrium, we investigate other features of the equilibrium, such as the Pareto effciency of the outcome and the relation with the Nash axiomatic approach.
The Borell-Ehrhard Game
A precise description of the convexity of Gaussian measures is provided by
sharp Brunn-Minkowski type inequalities due to Ehrhard and Borell. We show that
these are manifestations of a game-theoretic mechanism: a minimax variational
principle for Brownian motion. As an application, we obtain a Gaussian
improvement of Barthe's reverse Brascamp-Lieb inequality.Comment: 23 page
Breakdowns
We study a continuous-time game of strategic experimentation in which the players try to assess the failure rate of some new equipment or technology. Breakdowns occur at the jump times of a Poisson process whose unknown intensity is either high or low. In marked contrast to existing models, we find that the cooperative value function does not exhibit smooth pasting at the efficient cut-off belief. This finding extends to the boundaries between continuation and stopping regions in Markov perfect equilibria. We characterize the unique symmetric equilibrium, construct a class of asymmetric equilibria, and elucidate the impact of bad versus good Poisson news on equilibrium outcomes
Continuous-time limit of dynamic games with incomplete information and a more informed player
We study a two-player, zero-sum, dynamic game with incomplete information
where one of the players is more informed than his opponent. We analyze the
limit value as the players play more and more frequently. The more informed
player observes the realization of a Markov process (X,Y) on which the payoffs
depend, while the less informed player only observes Y and his opponent's
actions. We show the existence of a limit value as the time span between two
consecutive stages goes to zero. This value is characterized through an
auxiliary optimization problem and as the unique viscosity solution of a second
order Hamilton-Jacobi equation with convexity constraints
Dynkin games with incomplete and asymmetric information
We study the value and the optimal strategies for a two-player zero-sum
optimal stopping game with incomplete and asymmetric information. In our
Bayesian set-up, the drift of the underlying diffusion process is unknown to
one player (incomplete information feature), but known to the other one
(asymmetric information feature). We formulate the problem and reduce it to a
fully Markovian setup where the uninformed player optimises over stopping times
and the informed one uses randomised stopping times in order to hide their
informational advantage. Then we provide a general verification result which
allows us to find the value of the game and players' optimal strategies by
solving suitable quasi-variational inequalities with some non-standard
constraints. Finally, we study an example with linear payoffs, in which an
explicit solution of the corresponding quasi-variational inequalities can be
obtained.Comment: 31 pages, 5 figures, small changes in the terminology from game
theor
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