Impatience, Risk Propensity and Rationality in Timing Games

Impatience, Risk Propensity and Rationality in Timing Games Moojan Ghafurian and David Reitter moojan@psu.edu reitter@psu.edu The Pennsylvania State University University Park, 16802, USA Abstract often fail to follow the prescribed policy, and many real-life situations require good judgment on the spot. Previous work has suggested that risk propensity, an in- dividual variable, influences peoples decisions in similar games. Risk propensity introduces a bias that leads people to make decisions that are contrary to their interests. Yet, the actual implementation of risk propensity is unknown. For timing decisions, we propose a related heuristic, impatience, which causes people to act earlier than is advisable. The heuristic does not take expected utility into account. Games of timing reflect dynamic decision-making under un- certainty, as it takes place in many real-world situations, in- cluding health care, safety and security. Rather than making discrete decisions, participants choose one or more points in time that determine the outcome. We study individual’s biases and characteristics in such games of timing. We examine risk propensity as a personal preference affecting timing decisions and document a bias, impatience. Experiment 1 analyzes peo- ple’s strategy in timing games in relation to a rational model. Contrasting two cognitive models suggests that individuals ap- ply risk propensity to the probability distributions underlying short games and when unfamiliar with the situation, but that, over time, impatience takes over as a linear adjustment. In Ex- periment 2, impatient participants risk their incentive payment in order to play early, even if they receive no advantage from doing so. Keywords: Decision-making under uncertainty; Rationality; Patience; Risk propensity; Timing games Related Work Introduction Many real-world decisions concern the timing of one’s ac- tions. Good examples are common security or safety sce- narios that are subject to cost/risk tradeoffs–at which point in time should guards patrol a dangerous area? While driv- ing, how often we turn to look if a bicyclist has started to move while we are waiting to enter an intersection? Decision- makers need to judge risk under uncertainty and anticipate an opponents actions. Unlike in much work on decision-making, the decision when to act becomes just as important as how to act. Games of timing generalize such scenarios and allow us to investigate the pertinent question whether well-known effects from classical, discrete decision-making apply. In the study presented in this paper, we use games to ana- lyze timing behavior and correlate it with both estimated and survey-based measures of risk propensity (a preference for risk-seeking over risk-avoidance). In the first version of the game, a virtual opponent chooses the timing of a covert move. The player is to anticipate the opponent’s move and make his own move a shortly as possible afterward. Pre-empting the opponent is ineffective and costly to the player. Generally, all games we use involve stochastic, time-based moves by an opponent, and one game features a payoff dis- tribution that is not symmetric between early and late action. This is a characteristic of many real-life situations (e.g., in se- curity, safety or personal health, where acting early incurs a small penalty, but acting late leads to large losses). This game is representative of a wide range of situations. Some of these situations would be calculated and encoded in policies (i.e., what is the best interval for checking fire safety devices in a public place? How often and at what age should people un- dergo medical screening for hints of a disease? ) Yet, people Timing decisions have seen relatively limited attention com- pared to discrete decisions. We know that time is perceived differently by different people. E.g., impulsive individuals over-estimate the duration of time intervals, specially when they are waiting for a beneficial outcome of their action (Wittmann & Paulus, 2008). This makes timed decision- making particularly challenging for some people. Decision-maker’s motivations and understanding of the risks greatly influence the outcome of timing decisions. A case in point is health screening, where people differ greatly in their compliance with policies that optimize risks and ben- efits (Rakowski, Fulton, & Feldman, 1993; Sonnenberg & Beck, 1993). Understanding human biases in such timing de- cisions is key to successfully convince people to act rationally in preventative care. Recently, Reitter, Grossklags, and Nochenson (2013) used the FlipIt game of “stealth takeover” (van Dijk, Juels, Oprea, & Rivest, 2012) to relate risk propensity to decision-making under uncertainty in a dynamic, adversarial environment. In this game, players have to estimate the timing of multiple opponent moves and follow them (but not precede them) as closely as possible. Experiment 1 of this paper is a controlled equivalent to the very first move in FlipIt. We will consider rational solutions to the two games as the ones that optimize expected utility given currently available information. This contrasts with game-theoretic predictions, where individuals should, in repeated games, tend to choose equilibrium strate- gies (see Teraoka, 1983, for a duel-type timing game). Experiment 1 Experimental games allow us to observe behavior in situa- tions comparable to those mentioned above. We generally operationalize the timing situations as searching for an un- known event (happening in a specific period of time) when efforts for searching and latency in finding the event are both costly. During a round of l seconds duration, participants play