We are integrating game theory with stochastic process theory to formulate an Event-Driven Game Theory for decision making.

Traditional analyses of interacting decision makers typically employs a fixed clock where the precise times and order of decisions are fixed. In many real-world scenarios, that is not the case. Take a potentially vulnerable computer network, for example. In that case, there are many users accessing different parts of the network at different times while malicious attackers try to enter, exit, and traverse the network -- also at seemingly random times. We are trying to understand how uncertainty in when something might happen influences decision making behavior. As the old adage says, "timing is everything.” But how do we quantify exactly what "everything” means?

Decision makers often face uncertainty in their choices but also about when something might happen. For example, a large investment firm must choose not only which securities to transact but also the optimal time to make such transactions. To further complicate matters, the investment firm also faces uncertainty as to when other investment firms receive information and make transactions.

Game theory -- the standard quantitative tool for analyzing interacting decision makers --often proves insufficient for capturing the importance of random event sequences and timings. This project's foundational goal is to expand the tools of game theory to better capture the importance of uncertain timing and sequence of events.

This endeavor includes integrating game theory with stochastic process theory to formulate what we refer to as Event-Driven Game Theory. In our baseline formulation, the times in which decision makers receive information and act is randomly determined by an underlying stochastic process.

We have investigated the importance of timing uncertainty in domains ranging from computer network security to air traffic control to collusive cartel formation.

David Wolpert