Continuous-time Experiments Research Articles

Communication Among Harvesters Leads to Sustainable Fishing Behaviour in a Continuous Time Common Pool Resource Experiment

The sustainable use of common pool resources (CPRs) such as fisheries constitutes a major challenge for society. A large body of empirical studies conducted in discrete time indicates that resource users are able to prevent the ‘tragedy of the commons' under institutional arrangements that can promote cooperation. However, the variability exhibited by the human behaviour and the dynamic nature of renewable resources require continuous time experiments to fully explain the mechanisms underpinning the sustainable use of resources. We conducted CPR experiments in continuous time to investigate how the extraction behaviour of resource users changes in real-time in response to changes in resource availability under communication and no communication. We find that when communication is allowed, users adjust their extraction efforts based on knowledge of previous resource availability. In contrast, when communication is not allowed, users do not incorporate resource availability into their utility function. These results suggest that communication does not merely provide a forum for coordination but mediates a causal relationship between resource levels and extraction behaviour. Our findings may help the development of effective resource management policies.

Continuity, Inertia, and Strategic Uncertainty: A Test of the Theory of Continuous Time Games

The theory of continuous time games (Simon and Stinchcombe (1989), Bergin and MacLeod (1993)) shows that continuous time interactions can generate very different equilibrium behavior than conventional discrete time interactions. We introduce new laboratory methods that allow us to eliminate natural inertia in subjects' decisions in continuous time experiments, thereby satisfying critical premises of the theory and enabling a first-time direct test. Applying these new methods to a simple timing game, we find strikingly large gaps in behavior between discrete and continuous time as the theory suggests. Reintroducing natural inertia into these games causes continuous time behavior to collapse to discrete time-like levels in some settings as predicted by subgame perfect Nash equilibrium. However, contra this prediction, the strength of this effect is fundamentally shaped by the severity of inertia: behavior tends towards discrete time benchmarks as inertia grows large and perfectly continuous time benchmarks as it falls towards zero. We provide evidence that these results are due to changes in the nature of strategic uncertainty as inertia approaches the continuous limit.

Oligopoly Competition in Continuous Time

We conduct oligopoly competition experiments with differentiated goods in discrete and continuous time. Continuous time experiments allow for real-time, asynchronous strategic interaction and are therefore argued to be a more realistic mode of interaction, particularly in the context of (electronic) markets. We consider duopolies and triopolies both under Bertrand as well as Cournot competition and consistently find that, ceteris paribus, tacit collusion is higher under discrete time than under continuous time, which contrasts the theoretical prediction. Thus, our results bear important methodological implications for research on oligopoly competition.

Time Horizon and Cooperation in Continuous Time

We study social dilemmas in (quasi-) continuous-time experiments, comparing games with different durations and termination rules. We discover a stark qualitative contrast in behavior in continuous time as compared to previously studied behavior in discrete-time games: cooperation is easier to achieve and sustain with deterministic horizons than with stochastic ones, and end-game effects emerge, but subjects postpone them with experience. Analysis of individual strategies provides a basis for a simple reinforcement learning model that proves to be consistent with this evidence. An additional treatment lends further support to this explanation.

Emulation of n−trailer Systems through Differentially Driven Multi-Agent Systems: Continuous- and Discrete- Time Approaches

This paper proposes the emulation of a physical standard or generalized n?trailer through the decentralized control of a multi-agent system composed of several differentially driven mobile robots. The key point is to solve a time-varying version of the well known formation tracking or marching problem. The problem is solved both in discrete- and continuous-time cases. Four different control laws are proposed which require different variables to be available for feedback or feedforward, depending on the specifications of the experimental platform. The performance of the proposed control laws is illustrated through real-time experiments. It is shown that the discrete-time control law exhibits a performance comparable to that of the continuous-time control law with a sampling period 20 times larger than the one used in the continuous-time experiment.

Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment

Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment ∗ Timothy N. Cason † Daniel Friedman ‡ Ed Hopkins § Purdue University UC Santa Cruz University of Edinburgh July 19, 2012 Abstract We report laboratory experiments that use new, visually oriented software to ex- plore the dynamics of 3 × 3 games with intransitive best responses. Each moment, each player is matched against the entire population, here 8 human subjects. A “heat map” offers instantaneous feedback on current profit opportunities. In the continuous slow adjustment treatment, we see distinct cycles in the population mix. The cycle amplitude, frequency and direction are consistent with standard learning models. Cy- cles are more erratic and higher frequency in the instantaneous adjustment treatment. Control treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. Average play is approximated fairly well by Nash equilibrium, and an alternative point prediction, “TASP” (Time Average of the Shapley Polygon), captures some regularities that NE misses. JEL numbers: C72, C73, C92, D83 Keywords: experiments, learning, mixed equilibrium, continuous time. We are grateful to the National Science Foundation for support under grant SES-0925039, and to Sam Wolpert and especially James Pettit for programming support, and Olga Rud, Justin Krieg and Daniel Nedelescu for research assistance. We received useful comments from audiences at the 2012 Contests, Mech- anisms & Experiments Conference at the University of Exeter; Purdue University; and the 2012 Economic Science Association International Conference at NYU. In particular, we want to thank Dieter Balkenborg, Dan Kovenock, Dan Levin, Eyal Winter and Zhijian Wang for helpful suggestions. cason@purdue.edu, http://www.krannert.purdue.edu/faculty/cason/ dan@ucsc.edu, http://leeps.ucsc.edu E.Hopkins@ed.ac.uk, http://homepages.ed.ac.uk/hopkinse/

Probability learning of rats in continuous-time experiments

Probability matching behavior in time was shown by rats under two non-contingent reinforcement schedules (.50 and.625) with correction plus shock procedure but not with non-correction. Sequential data indicated that the maximum effect of reinforcement occurred about 6 sec. later and that only two preceding reinforcements were effective in determining response probability.