The strategic use of time in real-life games
Keywords: Management Science and Engineering.

This research enables decision makers to use time strategically in real-life games. At its core, it is pushing back against the assumption of an obvious decision time that is implicitly made when real-life situations are modeled as turn-based games with no sense of time. When analysts model real-life situations as turn-based, timing-free games, the application of the model's insight is stunted. The analyst has derived an optimal policy for what to do, but not when to do it, and since real-life situations rarely come with turns, a lot of the value can be lost. In every game, a first-person perspective is taken, since the model's main objective is to provide normative advice to a single decision maker. Throughout the game, a focus on the passage of time, which is discretized into time intervals, allows for players to better understand how their actions and choice of timing affect the situation. Players will often have a chance to act now or employ strategic patience, in which case they decide that waiting is their best alternative. If a player waits, the model considers the possibility of the environment changing, of a player learning more about an uncertainty, of a player's alternatives changing with time, and of an opponent taking the initiative. Players also have the ability to affect the timing of their opponents' actions, which is called controlling the tempo of the game. A player can control the tempo by control- ling the information available to other players, using hard constraints like deadlines that remove future alternatives, or providing incentives for quick or slow action. The ability to indirectly increase one's own expected utility through an opponent's tim- ing will prove to be very powerful, which is shown in three intentionally diverse case studies. The first case study explores how a coach can use the clock strategically in a basketball game. A coach can be strategically patient by instructing his team to shoot the ball later in the shot clock and can control the tempo of the game by having his team foul intentionally. The model uses a team's historical play-by-play data to construct a distribution over possession lengths and outcomes, which allows for specific team matchups to be explored. Here, the Indiana Pacers will be the decision maker and the Chicago Bulls will be the opponent. The model constructs an optimal offensive and defensive policy for the Pacers that could help them win an extra game per NBA season. The second case study explores how an investment banking firm can improve the results of its recruitment process for juniors interns by incentivizing quick responses from students. Multiple ways that a firm can control the tempo of the game are explored. Exploding offers prove to be ineffective since the best students will be strategically patient. Offers of decreasing value prove to be more effective since they both incentivize quick action and also do not expire when a student is patient. The specific decision maker explored here is the investment bank JP Morgan, who could see improvements in recruiting by using time strategically. The third case study explores how the United States could have used time strate- gically in the Cuban Missile Crisis. The work reconstructs from historical primary sources what was known/believed at the time by President Kennedy and his advisors. As the President waits, he learns more about the number of offensive weapons in Cuba and the feasibility of a diplomatic solution, but the Soviet surface-to-surface missiles are more likely to become operational. Both the US and the USSR are also uncertain about the other's willingness to escalate to a nuclear exchange/full-scale war. In this context, the model provides normative advice on both what to do and when to do it despite uncertainty over what the opponents wants, knows, and has. The effect of modeling the Soviet Union as less than rational is also discussed. The value of the case study is the framework through which an optimal policy for the United States can be derived; this framework could potentially be applied to a modern-day crisis in which timing plays a key role.