Discrete-time games reveal payoffs after both players stop, leading to new equilibrium strategies.
problem Non-zero-sum stopping games with delayed payoff revelation.
method Analyzes simultaneous and sequential stopping strategies, proving Nash equilibria in both cases.
result Existence of Nash equilibria in mixed and pure stopping strategies.
We consider a zero-sum continuous time stopping game in which the pay-off is revealed in the maximum of the two stopping times instead of the minimum, which is the case in Dynkin games.
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
A game where agents solve optimal stopping problems interactively.
problem Optimal stopping problems in a mean field game setting.
method Formulated a mean field stochastic game, solved with a continuum of agents, and identified equilibria through a simple equation.
result Equilibria identified and the dynamics in the population analyzed.
Study optimal stopping and a non-zero-sum game with risk measures in discrete time.
problem Optimal stopping and risk assessment in discrete time with non-zero-sum game.
method Using g-expectations and recursive procedures, construct Nash equilibrium. result Construct Nash equilibrium for a non-zero-sum game with risk measures.
We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time…
Paper develops a new method for game options in local volatility models.
problem Optimal stopping in one-dimensional diffusion with general coefficients.
method Skorokhod embedding to construct recombining tree approximations.
result Construct nearly optimal stopping times with convergence rates.
New Dynkin games with Poisson intervention times studied for convertible bond strategies.
problem Optimal stopping strategies for convertible bonds with random intervention times.
method Characterized by backward stochastic differential equations.
result Optimal conversion and calling strategies for convertible bonds derived.
Game options study gradual exercise and cancellation with transaction costs.
problem Analyzing game options with gradual exercise and cancellation under proportional transaction costs.
method Developed algorithmic constructions for bid and ask prices, superhedging strategies, and optimal mixed stopping times.
result Increased flexibility in hedging leads to tighter bounds on option price.
We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who c…
Study on robust Dynkin game over singular probabilities.
problem A game over mutually singular probabilities with singular technical difficulties.
method Proved value process coincidence, used approximations for stopping times.
result Value process is a submartingale up to first meeting time.
Study on games with degenerate diffusion matrices, proving value existence and convergence.
problem Zero-sum games between singular controller and stopper with degenerate diffusion.
method Probabilistic approach using parameterized approximations, convergence analysis.
result Existence of value and optimal stopping times for the game with degenerate dynamics.
Study shows convergence of Nash equilibria to mean field game limit.
problem Convergence of Nash equilibria to mean field game limit in games of optimal stopping.
method Analysis of convergence of n-player equilibria to mean field equilibria. result Mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but not all mean field equilibria are limits. We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\…
We study the existence of optimal actions in a zero-sum game infτsupPEP[Xτ] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem infτE(Xτ) for a class of sublinear expectations E(⋅) such as the G-expectation. We show that …
Study proves value of non-Markovian games with partial, asymmetric info.
problem Value of non-Markovian Dynkin games with partial and asymmetric information.
method Probabilistic and functional analytic approach based on Sion's min-max theorem.
result Existence of optimal strategies for both players in randomised stopping times.
Study a game for pricing options with uncertain asset returns.
problem Pricing options on assets with unknown return rates.
method Reduction to a Dynkin game on a bi-dimensional diffusion, use filtering techniques.
result Existence of Nash equilibrium in pure strategies for stopping times.
The paper shows failure of smooth pasting principle in time-inconsistent stopping problems.
problem Time-inconsistent stopping problems with non-constant time preference rates.
method Analysis of the smooth pasting principle within the intra-personal game theoretic framework.
result The smooth pasting principle fails under time-inconsistency and does not guarantee equilibrium solutions.
In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximiza…
Market microstructure model with speculators who deduce asset value from prices.
problem Modeling market microstructure with agents who deduce asset value from prices.
method Control-stopping games and coupled control-stopping problems (RBSDEs).
result Existence of a solution to the system of coupled control-stopping problems.
New algorithm finds optimal sample complexity for pure exploration with multiple good answers.
problem Determining the optimal number of samples needed to explore multiple good answers in a bandit problem.
method Derive lower bound using game equilibrium, extend Track-and-Stop algorithm to multiple answers.
result New algorithm has asymptotic sample complexity matching the derived lower bound.
Solves game contingent claims using Nash equilibria in incomplete markets.
problem Analyzing game contingent claims in incomplete markets with utility-based hedging.
method Solves the stochastic game corresponding to GCCs with both stopping and trading, constructing Nash equilibria.
result Constructs Nash equilibria for GCCs with utility-based hedging, extending existing literature.
Early stopping method saves up to 75% computation time in policy search tasks.
problem Lengthy evaluation times in optimization problems, especially in robotics.
method A generalized early stopping criterion that only uses objective value at each time step.
result The method saves up to 75% computation time compared to no stopping.
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 …
On a filtered probability space (Ω,F,P,F=(Ft)t=0,…,T), we consider stopper-stopper games $\overline V:=\inf_{\Rho\in\bT^{ii}}\sup_{τ\in\T}\E[U(\Rho(τ),τ)]$ and $\underline V:=\sup_{\Tau\in\bT^i}\inf_{ρ\in\T}\E[U(\Rho(τ),τ)]$ in discrete time, where U(s,t) is $\mathcal{F}_{s\vee…
Study examines strategic exit timing in uncertain competition.
problem Timing of strategic exit decisions in competitive markets with uncertainty.
method Constructs a stochastic game equilibrium for exit strategies involving state variable and posterior belief process.
result Unique equilibrium found for symmetric Bayesian players.
Study callable convertible bonds with liquidity constraints, generalizing previous work.
problem Callable convertible bond problem with liquidity constraints.
method Introduced a new technique to handle non-ordered payoff situations.
result Complete solution to callable convertible bond problem with liquidity constraint.
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary o…
Study on optimal strategies for minimizing shortfall risk in game options.
problem Existence of optimal hedging strategies for shortfall risk in game options.
method Continuous time Black--Scholes model, finite and infinite exercise times.
result Optimal strategies exist for finite exercise times but not for all time intervals.
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent …
The paper analyzes a game where players must balance short-term and long-term interests, leading to cooperative or competitive outcomes.
problem Analyzing time inconsistency in inter-personal decision-making under non-exponential discounting.
method Iterative procedures and Zorn's lemma to find Nash equilibria between players' intra-personal equilibria.
result Inter-personal equilibria exist and depend on the impatience levels of the players.
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
Optimal exit strategies of CPT gamblers in unfair gambles
problem Optimal exit strategies of gamblers with CPT preferences in games with strictly negative expected payoffs
method Formulating the problem as an optimal stopping problem on asymmetric random walks, applying geometric transformation, randomized strategies, and changing the decision variable
result The unfair problem in the infinite time horizon has finite values for a wide range of CPT parameter specifications
Deep learning improves reinforcement learning in video games.
problem Challenges in reinforcement learning with high-dimensional inputs.
method Used deep Q-network and batch normalization to improve reinforcement learning.
result Some agents learned to play T-rex Runner better than human experts.
Paper studies constrained control games with a novel approximation method.
problem Games with constrained control directions.
method Approximation procedure based on L1-stability estimates and almost sure convergence. result Existence of game's value and optimal strategy for the stopper.
The aim of this paper is twofold. First, we extend the results of [33] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar to the ones in [10], and when the two barriers are completely separated, we prov…
This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Le…
New theorem guarantees approximate equilibrium in non-convex games.
problem No guarantee of equilibrium in non-convex games.
method Introduced a minimax theorem for non-convex games involving neural networks.
result Provided an approximate minimax theorem for non-convex games.
This paper studies the valuation and optimal strategy of convertible bonds as a Dynkin game by using the reflected backward stochastic differential equation method and the variational inequality method. We first reduce such a Dynkin game to an optimal stopping time problem with state constraint, and then in a Markovian…
We study the problem of super-replication for game options under proportional transaction costs. We consider a multidimensional continuous time model, in which the discounted stock price process satisfies the conditional full support property. We show that the super-replication price is the cheapest cost of a trivial s…
Paper analyzes convergence rates for multi-agent learning in games.
problem Convergence rates for multi-agent learning in games.
method Characterizes finite-time convergence rates for joint OGD learning on λ-cocoercive games and develops adaptive algorithms. result Adaptive algorithms achieve same convergence rates as non-adaptive counterparts.
Winning solution for predicting player churn in a video game.
problem Predicting when players will stop playing a game.
method Long Short-Term Memory (LSTM) approach and conditional inference survival ensemble model.
result Models accurately predicted player churn and were robust to changing business models.
Paper proves a new lower bound on calibration error for binary prediction.
problem Proving a strong lower bound on calibration error for binary prediction.
method Developed two new techniques: early stopping and sidestepping.
result Proves an Ω(T0.528) lower bound on calibration error. Study bounds for prices of European and American options with optional termination.
problem Bounding prices of options with potential termination.
method Duality results linking upper prices of vulnerable options to American options with constrained exercise times.
result Linking upper prices of vulnerable options to American options and game options.
New learning dynamics achieve fast convergence in games without needing to know utility scales.
problem Fast convergence guarantees in learning games require prior knowledge of utility scales.
method Developed scale-free and scale-invariant learning dynamics using optimistic follow-the-regularized-leader with adaptive learning rates and clipping techniques.
result Achieved fast convergence rates to Nash and correlated equilibria without prior utility scale knowledge.
Survival ensembles improve churn prediction in mobile social games.
problem Predicting user churn in mobile social games to retain players.
method Survival analysis and ensemble learning techniques.
result Survival ensembles provide more accurate and robust churn predictions.
We study the solution's existence for a generalized Dynkin game of switching type which is shown to be the natural representation for general defaultable OTC contract with contingent CSA. This is a theoretical counterparty risk mitigation mechanism that allows the counterparty of a general OTC contract to switch from z…