3 research outputs found
Stochastic Switching Games and Duopolistic Competition in Emissions Markets
We study optimal behavior of energy producers under a CO_2 emission abatement
program. We focus on a two-player discrete-time model where each producer is
sequentially optimizing her emission and production schedules. The
game-theoretic aspect is captured through a reduced-form price-impact model for
the CO_2 allowance price. Such duopolistic competition results in a new type of
a non-zero-sum stochastic switching game on finite horizon. Existence of game
Nash equilibria is established through generalization to randomized switching
strategies. No uniqueness is possible and we therefore consider a variety of
correlated equilibrium mechanisms. We prove existence of correlated equilibrium
points in switching games and give a recursive description of equilibrium game
values. A simulation-based algorithm to solve for the game values is
constructed and a numerical example is presented.Comment: Revised version, 24 page
Unilaterally Competitive Multi-Player Stopping Games
A multi-player competitive Dynkin stopping game is constructed. Each player
can either exit the game for a fixed payoff, determined a priori, or stay and
receive an adjusted payoff depending on the decision of other players. The
single period case is shown to be "weakly unilaterally competitive". We present
an explicit construction of the unique value at which Nash and optimal
equilibria are attained. Multiple period generalisations are explored. The game
has interpretations in economic and financial contexts, for example, as a
consumption model with bounded resources. It also serves as a starting point to
the construction of multi-person financial game options. In particular, the
concept of optimal equilibria becomes pivotal in the pricing of the game
options via super-replication.Comment: 25 pages, 2 figure
Dynkin Games and Israeli Options
We start briefly surveying research on optimal stopping games since their
introduction by E.B.Dynkin more than 40 years ago. Recent renewed interest to
dynkin's games is due, in particular, to the study of Israeli (game) options
introduced in 2000. We discuss the work on these options and related derivative
securities for the last decade. Among various results on game options we
consider error estimates for their discrete approximations, swing game options,
game options in markets with transaction costs and other questions.Comment: survey articl