Optimal stopping behavior with relative ranks: the secretary problem with unknown population size

Seale, Darryl A.; Rapoport, Anatol

doi:10.1002/1099-0771(200010/12)13:4<391::aid-bdm359>3.0.co;2-i

Cited by 79 publications

(56 citation statements)

References 18 publications

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“…A variety of models have been developed for this tradeoff in many different contexts. They range from the idea of satisficing (Simon, 1990) and derived Bayesian satisficing models (Fu & Gray, 2006) to sequential heuristic models of optimal stopping (Seale & Rapoport, 2000), mutual mate choice (Todd & Miller, 1999), Bayesian optional stopping models (Edwards, 1965), Bayesian observer models (Vul et al, 2009), the accumulation of evidence to a threshold criterion (Busemeyer & Townsend, 1993;Ratcliff, 1978;Vickers, 1979), and models based on cognitive architectures for dynamic decision making (Gonzalez & Dutt, 2011;Gonzalez, Lerch, & Lebiere, 2003) During an exploitation to exploration tradeoff, the agent faces the question of how long to continue exploiting a current option and thereby obtain its rewards, and when to switch to exploring alternatives and thereby increasing the chance to find potentially better options elsewhere. Perhaps the most prominent model of this tradeoff, the marginal value theorem (MVT; Charnov, 1976), comes from the foraging literature where research has long attempted to formalize optimal behavior (Stephens & Krebs, 1987).…”

Section: Transitions Between Exploration and Exploitationmentioning

confidence: 99%

“…Optimal stopping behavior and search/choice strategies are affected by the horizon of a choice problem (Kaelbling et al, 1996); with horizons ranging from finite (where the agent knows there will be n choice-episodes: Lee et al, 2011), to uncertain (where the agent knows there will be somewhere between n and m episodes : Seale & Rapoport, 2000), to infinite (where the agent knows there is a probability of any episode being the final one, but the actual number of episodes is neither known nor constrained to fall within any range: Gittins, 1979). Internal (Memory) vs.…”

Section: Factormentioning

confidence: 99%

See 1 more Smart Citation

Unpacking the exploration–exploitation tradeoff: A synthesis of human and animal literatures.

Mehlhorn¹,

Newell²,

Todd³

et al. 2015

Decision

326

318

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Many decisions in the lives of animals and humans require a fine balance between the exploration of different options and the exploitation of their rewards. Do you buy the advertised car, or do you testdrive different models? Do you continue feeding from the current patch of flowers, or do you fly off to another one? Do you marry your current partner, or try your luck with someone else? The balance required in these situations is commonly referred to as the exploration-exploitation tradeoff. It features prominently in a wide range of research traditions, including learning, foraging, and decisionmaking literatures. Here, we integrate findings from these and other often-isolated literatures in order to gain a better understanding of the possible tradeoffs between exploration and exploitation, and we propose new theoretical insights that might guide future research. Specifically, we explore how potential tradeoffs depend on (1) the conceptualization of exploration and exploitation; (2) the influencing environmental, social, and individual factors; (3) the scale at which exploration and exploitation are considered; (4) the relationship and types of transitions between the two behaviors; and (5) the goals of the decision maker. We conclude that exploration and exploitation are best conceptualized as points on a continuum, and that the extent to which an agent's behavior can be interpreted as exploratory or exploitative depends upon the level of abstraction at which it is considered.

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Section: Transitions Between Exploration and Exploitationmentioning

confidence: 99%

Section: Factormentioning

confidence: 99%

Unpacking the exploration–exploitation tradeoff: A synthesis of human and animal literatures.

Mehlhorn¹,

Newell²,

Todd³

et al. 2015

Decision

326

318

View full text Add to dashboard Cite

show abstract

“…In both cases, researchers took a well-established optimality paradigm, then analyzed and explained the systematic deviations from optimality that they observed in actual behavior. Other related papers in other contexts include Houser, Keane, and McCabe (2004), Hutchinson and Meyer (1994), Neslin and Greenhalgh (1983), and Seale and Rapoport (2000).…”

Section: Introductionmentioning

confidence: 99%

The Traveling Salesman Goes Shopping: The Systematic Deviations of Grocery Paths from TSP-Optimality

2008

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We examine grocery shopping paths through the lens of the "Traveling Salesman Problem" (TSP), a classic paradigm from the field of operations research. We define the "TSP-optimal" path for each shopper as the shortest path that connects all of his purchases, and we study the systematic deviations seen in his actual behavior. We decompose the length of each observed path into three components: the length of the TSP-optimal path, the additional distance due to order deviation (i.e., not following the TSP-optimal order of category purchases), and the additional distance due to travel deviation (i.e., not following the shortest point-to-point paths).We then explore the relationship between these deviations and purchase behavior. Among other things, our results show a strong relationship between order deviation and basket size, but no association between travel deviation and basket size. Finally, we look at the implications of relaxing three of the rigid assumptions of the TSP by allowing for: (1) varying degrees of "forward-lookingness" across shoppers based on their observed order of purchases, (2) the possibility of unplanned purchases, and (3) the possibility of planned category visits but no resulting purchases.1

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“…This observation, however, does not indicate that their stopping rule is necessarily close to the optimal rule -it could also be that the payoff to search tasks is not very sensitive to deviations from the optimal stopping strategy (see Harrison and Morgan, 1990;Rapoport, 1997, 2000). Overall, while people seem to behave as predicted by theory when parameters of the search environment change (e.g., Schotter and Braunstein, 1981), experimental findings in various search contexts suggest that individuals tend to search too little relative to the optimal strategy (Hey, 1987;Cox and Oaxaca, 1989;Houser and Winter, 2004;Seale and Rapoport, 2000;Sonnemans, 1998). Cox and Oaxaca suggest that this might be traced back to risk-averse behavior of the individuals (Cox and Oaxaca, 1989).…”

mentioning

confidence: 99%

The relationship between risk attitudes and heuristics in search tasks: A laboratory experiment

Schunk¹,

Winter²

2009

Journal of Economic Behavior & Organization

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Experimental studies of search behavior suggest that individuals stop searching earlier than predicted by the optimal, risk-neutral stopping rule. Such behavior could be generated by two different classes of decision rules: rules that are optimal conditional on utility functions departing from risk neutrality, or heuristics derived from limited cognitive processing capacities and satisficing. To discriminate among these two possibilities, we conduct an experiment that consists of a standard search task as well as a lottery task designed to elicit utility functions. We find that search heuristics are not related to measures of risk aversion, but to measures of loss aversion.

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Optimal stopping behavior with relative ranks: the secretary problem with unknown population size

Cited by 79 publications

References 18 publications

Unpacking the exploration–exploitation tradeoff: A synthesis of human and animal literatures.

Unpacking the exploration–exploitation tradeoff: A synthesis of human and animal literatures.

The Traveling Salesman Goes Shopping: The Systematic Deviations of Grocery Paths from TSP-Optimality

The relationship between risk attitudes and heuristics in search tasks: A laboratory experiment

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