Competing for congestible goods: experimental evidence on parking choice

Congestible goods, characterized by excludability and rivalry, act as public goods under low demand and common-pool resources when crowded. Examples include education, healthcare, and parking. Parking is a significant urban issue, contributing substantially to traffic congestion and pollution. Current efforts focus on technological solutions like real-time parking availability information. This paper complements these efforts by investigating the decision-making process of drivers choosing parking lots, framing it within game theory. Previous research has addressed driver heuristics and recommended strategies, but lacks an experimental investigation of real human decision-making. This study aims to fill this gap and inform the design of effective parking facilities. The experiment involves participants choosing between a convenient, limited-spot parking lot and a less convenient, unlimited-spot one. The Nash equilibrium predicts the number of participants competing for the convenient lot based on the number of spots, and the costs involved. The research question is whether this prediction holds and what insights into human behavior can improve urban parking planning.

The paper reviews existing literature on congestible goods, highlighting their characteristics and examples. It mentions the "tragedy of the commons" and discusses various approaches to manage congestible goods, particularly parking. The authors cite studies on parking behavior, heuristics used by drivers, and models of decision-making under bounded rationality. A gap in the literature is identified: the lack of experimental studies on human decision-making in parking lot selection. The paper positions itself as filling this gap by experimentally investigating this strategic decision.

The experiment involved 240 participants (with 36 dropouts) in groups of 20, playing four repetitions of a game with different parameters. In each repetition, participants made ten parking choices between a "yellow" (convenient, limited) and a "blue" (inconvenient, unlimited) lot. The yellow lot had either 5 or 10 spots. Costs included parking fees for both lots and an additional cost if the yellow lot was full. Eight treatments resulted from combining different numbers of spots (S), cheap parking cost (Q_cheap), expensive parking cost (Q_exp), and additional cost (Q_add). Participants received 100 points per round and were paid if they completed at least 70% of the decisions. After each round, participants received feedback on their choices and the number of people who successfully parked in the yellow lot. A risk assessment test was administered after the experiment. Data analysis focused on participant-made decisions, with random decisions (due to timeouts or dropouts) replaced by randomly selected decisions from the same treatment and round. Analysis involved comparing the average number of participants choosing the yellow lot in each treatment with Nash equilibrium predictions and conducting statistical tests (ANOVA and Tukey's range test) to determine if differences between treatments were significant. Risk aversion data was also analyzed to see if it correlated with competitive behavior.

The Nash equilibrium accurately predicted behavior only when the yellow lot had few spots (S/N=0.25). When more spots were available (S/N=0.5), the Nash equilibrium overestimated the number of participants choosing the yellow lot. Participants exhibited more cautious behavior than predicted by the Nash equilibrium, particularly when the yellow lot had more availability. The Rosenthal equilibrium, which incorporates bounded rationality and accounts for randomness in decision-making, provided a better fit to the experimental data. The rationality parameter (t) in the Rosenthal model indicated a degree of randomness in the decision process, with t=0.05 providing a good fit for most cases and t=0.02 for the most complex scenarios. An agent-based model using reinforcement learning successfully replicated the experimental results, showing convergence to a stable behavior similar to the Rosenthal equilibrium prediction. The model also captured the speed at which this convergence occurred. No correlation was found between participants' risk aversion and their competitive behavior. The findings suggest that the limited-spot parking strategy is superior in directing the traffic compared to having numerous spots available, in contrast to the prediction of the Nash equilibrium.

The study's findings challenge the applicability of the Nash equilibrium in predicting human behavior in congestible goods situations, especially when choices are complex and involve uncertainty. The Rosenthal equilibrium and reinforcement learning model offer more accurate and insightful explanations, emphasizing bounded rationality and the influence of randomness. The better prediction of the Rosenthal model compared to the Nash equilibrium model reinforces the limited rationality hypothesis, suggesting that decision-makers don’t always make perfectly rational choices but instead incorporate factors such as the cost of the effort involved in selecting an optimal option. The results provide valuable insights into human decision-making processes, suggesting the need for models that incorporate bounded rationality. Furthermore, the convergence to equilibrium behavior in the reinforcement learning model is consistent with real-world scenarios, supporting the use of such models in decision-making problems under uncertainty.

The study demonstrates that the Nash equilibrium is not sufficient to predict human behavior in congested parking lot selection problems. Both the Rosenthal model with a rationality parameter t in the range [0.02, 0.1] and a reinforcement learning dynamic model offer significantly better predictions. The results suggest that limited-spot parking lots are more effective than unlimited-spot ones in managing demand, providing valuable insights for urban planning and the design of parking facilities. Further research could explore different parameters, including the cost of time and spatial heterogeneity of parking demand, to refine the model and improve the understanding of parking behavior. The methodologies introduced could be used to model and predict behavior in other congestible good situations.

The study was conducted online, which might not perfectly capture real-world parking scenarios. The limited range of parameters may not fully generalize to all contexts. The sample size, while relatively large, could be further increased for greater statistical power. Future studies should also consider incorporating more realistic factors that influence parking choice, such as drivers’ perceptions of risk, social norms, and the availability of information on alternative parking options.