Log in. Namespaces Page Discussion. Views View View source History. Jump to: navigation , search. References [1] L. Shapley, "Stochastic games" Proc. Gillette, "Stochastic games with zero stop probabilities" , Contributions to the theory of games , 3 , Princeton Univ. Press pp. Parthasarathy, M. Stern, "Markov games: A survey" E. Roxin ed. Liers ed. Sternberg ed. Dekker pp. Behavior tended to be risk loving when artificial monetary prizes were used or when there was minimal uncertainty in the natural non-monetary outcome.
But subjects drawn from the same population were risk averse when their attitudes were elicited using the natural nonmonetary outcome that had some background risk.
Theory predicts this effect of background risk, but not the change from risk-loving to risk-aversion. Recently, economists have developed methods for structural estimation of auction models. Many researchers object to these methods because they find the rationality assumptions used in these models to be implausible. In this paper, we explore whether structural auction models can generate reasonable Abstract - Cited by 55 5 self - Add to MetaCart Recently, economists have developed methods for structural estimation of auction models.
Using bid data from auction experiments, we estimate four alternative structural models of bidding in first-price sealed-bid auctions: 1 risk neutral Bayes-Nash, 2 risk averse Bayes-Nash, 3 a model of learning and 4 a quantal response model of bidding.
For each model, we compare the estimated valuations and the valuations assigned to bidders in the experiments. Sophisticated Experience-Weighted Attraction learning and strategic teaching in repeated games by Colin F. Most learning models assume players are adaptive i. Empirical evidence suggests otherwise. In this paper, we extend our adaptive exper In this paper, we extend our adaptive experience-weighted attraction EWA learning model to capture sophisticated learning and strategic teaching in repeated games.
The generalized model assumes there is a mixture of adaptive learners and sophisticated players. An adaptive learner adjusts his behavior the EWA way.
A sophisticated player rationally best-responds to her forecasts of all other behaviors. A sophisticated player can be either myopic or farsighted. We estimate the model using data from p-beauty contests and repeated trust games with incomplete information. The generalized model is better than the adaptive EWA model in describing and predicting behavior. Including teaching also allows an empirical. A model of noisy introspection by Jacob K. Holt - Games and Economic Behavior , This paper presents a theoretical model of noisy introspection designed to explain behavior in games played only once.
The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported.
The accuracy of the model is compared with that of several alternatives. On the empirical content of quantal response equilibrium by Philip A. Palfrey has recently attracted considerable attention, due in part to its widely documented ability to rationalize observed behavior in games played by experimental subjects.
However, even with strong a priori We have chosen a simple example so that in either state choice 1 always gives a lower payoff than choice 2. The procedure for determining the Nash equilibrium and social optimum for a stochastic game such as this is outlined in the Appendix. The long-term equilibrium is for the players to be in state 2, both earning the maximum reward of 8 at each time point. Since a player can increase their payoff by defecting from the social optimum, it cannot be a Nash equilibrium.
Figure 3. The solution to a simple stochastic game representing resource competition showing the Nash equilibrium blue triangles and social optimum red triangles. The states of the stochastic game are a high resource and low resource state and the pure strategies available to the players are to in either state to either be a Greedy or Moderate user of the resource.
For the stochastic game we assume voluntary test adoption of the new diagnostic ELISA test under a given perfect test regime, assuming a perfect test sensitivity and test specificity [see Supplementary Material for implementation of a multi-state setup under an imperfect test regime 26 ].
Based on infestation status and test adoption decisions taken the previous year, a farm may be at high, medium, or low risk of infestation this year. In the model, last year's decisions and infestation status determine the decisions the farmer takes this year, and along with the resulting farmer payoffs. To determine the payoffs, we used epidemiological parameters and estimated costs associated with sheep scab prevalence, which were derived from the literature 2 , 5 , 11 and are summarized in Tables 1 , 2.
Traditional treatment costs were obtained for two different treatments, organophosphate plunge dipping and an injectable formulation using a macrocyclic lactone. Subsequent results are presented for the slightly cheaper option of dipping. Table 1. Sheep scab economic costs and epidemiological parameters derived from literature. Costs per head in Table 1 are derived from reported flock costs 2. Thus, the new test is 1. Note that the values for the stage payoffs are determined by what the farmer perceives his risk of infestation to be, which may not be an accurate reflection of reality.
We considered four scenarios for the test-adoption game:. At this point infestation will be identified and the whole flock will be treated at cost C Treat. Therefore, under scenario 2, the farmer's payoff, P 2 , would be. Under scenario three, the test costs C Test are included for the calculation of the stage pay-off P 3 ,where. Under scenario 4, using the diagnostic test and treating infested animals prevents the flock from progressing to the clinical state. Another consideration is that because the farmer does know whether his flock is infested or not, he derives his decision to adopt the test or not from what he anticipates his payoff to be.
Here, we assume that the farmer is risk neutral and therefore that expected payoffs are a linear combination of the payoffs for an infected and uninfected flock. If he decides to adopt the test, his anticipated or expected pay-off would be a weighted average of that under scenarios 3 and 4 i. Table 3. The data available for these farms was their current infection status and the number of outbreaks in the previous 10 years [illustrated in Figure 1 of 5 ].
This model fitting therefore exploits the temporal autocorrelation in these data. In order to decide whether the farmers will consider themselves in a high, medium, or low risk state next season depends on the possible outcomes for this season which in turn depend on the farmers' actions. At the end of the season, the four possible outcomes allowing for an imperfect test for a flock are:.
Outcome 1 clinical infestation is observed and treated will occur if a flock is infected and also progressed to clinical infestation without the farmer having tested the flock. Outcome 2 subclinical infestation is correctly identified and treated will happen if the flock was infected and tested positive.
Outcome 3 subclinical infestation is incorrectly identified will occur if the flock was uninfected and testing results in a false positive. Outcome 4 no infestation is observed will happen if the flock is uninfected and testing returns no false positives. If the farmer does not adopt the test, infestation can only be identified at the clinical stage.
The outcomes described above determine whether a farmer is in a high, medium, or low risk state next season. In other words, the outcomes determine the probabilities of transitioning to the high, medium or low risk state.
L ij gives the probability of transition to the low risk state next season given outcome i for the farm 1 and outcome j for the farm 2. Similarly, M ij gives the probability of transition to the medium risk state next season given outcome i for the farm 1 and outcome j for farm 2.
H ij gives the probability of transition to the high risk state next season given outcome i for the farm 1 and outcome j for the farm 2. As an example, consider a scenario in which neither farmer adopts the test.
Therefore, the probability of these observations and followed by transitioning to the high-risk state next season would be. Thus, the overall probability of transition to the high-risk state will be obtained by summing over all i and j , i. Accordingly, for the complete stochastic game, the final payoff matrices and transition probabilities for the high risk state blue , medium risk state orange , and low risk state green are defined in Table 4.
We first examined the test adoption decision for each assumed risk state high, medium, low in terms of the Nash equilibrium and as a function of the extent to which farmers value future profits. Whenever a farmer considers their farm to be at high risk, i. Whenever a farmer considers their farm to be at low risk, i.
However, when a farmer considers their farm to be at medium risk i. In this case, mixed adoption can also be observed, meaning that the farmer will adopt the test with some probability between 0 and 1. Figure 4. The Nash equilibrium probability in each of the three states high, medium, and low risk of adopting the new ELISA test when the cost is 1. The test costs would need to more than double before test adoption is not always observed in the high-risk state see Figure 5B , and would need to be very low before test adoption can be seen in the low-risk state see Figure 5C.
Figure 5. The Nash equilibrium probability in each of the three states high, medium, and low risk of adopting the new ELISA test as a function of the discount factor for different multiples of the status quo clinical diagnosis cost A medium test costs, shown for multiples of 1.
We found that the Nash equilibrium strategy does not always match the social optimum. For the same parameters as for Figure 4 i. Figure 6. The Nash equilibrium blue triangles and the social optimum red triangles for a test cost 1. The test adoption decision determines the amount of time spent by the farms in the high-, medium-, and low-risk states Figure 7. At the Nash equilibrium Figure 7 , blue triangles , compared to the status quo Never adopt , less time is spent in the high-risk state, and more time spent in the medium and low-risk states.
Compared to the Nash equilibrium, the social optimum Figure 7 , red triangles either equals the Nash equilibrium or improves upon it by spending less time in the high-risk state and more time in the medium- and low-risk states. Figure 7. Figure 8. Contrasting the extreme cases of a discount factor of 0 a short-term outlook and a discount factor of 1 a long-term outlook , shows the epidemiological outcome to be relatively robust to the discount factor.
Figure 9. The expected profits per head are greatest for the strategy of adopting the test in the high and medium risk state the Nash equilibrium and social optimum for the long-term outlook; Figure The gains are relatively small, but nevertheless these results show that substantial reductions in annual incidence can be achieved without increasing costs to the farmer. Figure In this case of the long-term outlook, the Nash equilibrium and social optimum coincide at test adoption in the high and medium risk state shown in red.
The transmission and control of infectious diseases strongly depends on both the individual and joint decisions people make with regard to control measures and treatments. In this paper, we applied a game-theoretic model to examine the outcome of strategic interactions between neighboring farms, surrounding decisions to adopt a diagnostic test.
The term strategic interaction is used because each farmer's decision and payoff depends on the decision made by their neighbor. Specifically, the game-theoretic model applied in this paper was a stochastic game used to assess whether farmers are likely to adopt the new P. Via the discount factor, a stochastic game also allows us to account for farmer preferences in terms of whether they take a short-term or long-term outlook and correspondingly whether they only factor immediate payoffs into their test adoption decision, or whether they factor in future benefits.
In Scotland, the status quo is that sheep scab diagnosis happens through skin scraping by a veterinary surgeon. We analyzed the test adoption outcomes Nash equilibria and showed that that they are strongly-dependent on the assumed risk state high, medium, low , and also that they are modulated not just by the costs of the new diagnostic test but also by how much short-term profits are preferred over long-term benefits.
We found the outcomes in terms of test adoption to be relatively robust to the cost of the test, with substantial increases or decreases in test cost required to change the overall pattern of test adoption. Individual decisions in game-theoretic models are based on assumptions of rational self-interest and do not necessarily correspond to a socially optimal outcome. However, in our analysis, we found that test adoption decisions at the Nash equilibrium were socially optimal for most calculated outcomes.
Specifically, whenever a farmer considered their farm to be at high risk based on last year's infestation status of themselves or their neighbor's they always chose to adopt the new diagnostic test. Analogously, whenever a farmer considered their farm to be at low risk given that neither farm had sheep scab the previous year, the test was never adopted. One reason for this is that adopting the new diagnostic test is freely chosen by the individual farmers and individual choices do not necessarily align with the public interest.
Also, some individuals may free-ride on the protection provided by their neighbor, which is at odds with the socially optimal outcome. In light of this any new policy intervention promoting the use of the new diagnostic ELISA must address the divergence between private and public consequences of actions and, ideally, motivate individual free choice toward a social optimum This could be achieved for example by offering private incentives and encouraging cooperative schemes among farmers.
However, when viewing the outcomes in terms of the prevalence of infestation, we see that the outcomes are largely robust to whether the Nash equilibrium or social optimum is adopted.
The financial benefits to the farmer are not substantial; however, what these results show is that substantial reductions in sheep scab incidence should be achievable without additional costs to the farming community. Moreover, the results suggest that the primary goal should be to facilitate test adoption amongst farms at high-risk of infestation, as this would provide most of the epidemiological benefits.
However, there are limitations to this modeling framework. Firstly, the framework does not account for the fact that the external risk to farms should decline as the expected prevalence of infestation in the farms adopting the test declines.
Whilst capturing this would be desirable, it is not something that can readily be done within the stochastic game framework. We therefore view our results as a conservative assessment of the benefits of the adopting the test, since widespread adoption would reduce the external risk to farms.
Thus, cooperative behavior among the farming community should provide additional benefits, first by encouraging the social optimum rather than just the Nash equilibrium outcome, and secondly, by reducing the external risk of infestation and therefore the expected prevalence of infestation following widespread test adoption. A second limitation is that the model considers a two-farm system only and the above scenario of widespread adoption should ideally be assessed by extending the analysis to include multiple farms as well as multiple farmer strategies.
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