Karp Hordijk, A.

### 3 editions of this work

Kallenberg Moeschlin and D. Kohlberg, E. Repeated Games with Absorbing States, Ann. Kumar P. Shiau Liggett, T. Lippman Maitra, A. Parthasarathy On Stochastic Games, J. Mertens, J. Neyman Stochastic Games, Int. Game Theory , 10 , 53— Mohan, S.

Raghavan Monash, C. Thesis, Harvard University, Cambridge, Mass. Moulin, H. Vial Game Theory , 7 , — Nowak, A.

### ISBN 10: 1441951148

Theory Appl. Operations Research.

Ornstein, D. Soc , 20 , — Parthasarathy, T. Tijs and O. Moeschlin, and D. Pallaschke, —, Springer-Verlag, Berlin. Pollatschek, M. Raghavan, T. Tijs, and O. To foreshadow the results of our detailed analysis, we summarize the key findings of the paper as follows. A key factor behind this difference is that subjects in the SPD games respond not just to what their counterparts did, but also to whether or not they suffered a loss. However, we found that the pattern of cooperation was different in the two types of games.

The remainder of the paper proceeds as follows. After characterizing our experimental design for a set of controlled laboratory experiments Section 4 , we then specify a set of between-treatment hypotheses and test them using regression analysis Section 5. In Section 6, we build a Bayesian hierarchical model that enables us to test hypotheses with respect to within-subject behavior. Section 7 summarizes the findings, discusses their prescriptive implications and suggests areas for future research.

**http://www.grenadarevoconference2019.com/images**

## Stochastic Games — An Overview

The Appendix provides the details of our experiments, making them reproducible by others interested in studying stochastic IDS games. In a single period DPD game, defecting is the only Nash equilibrium and experiments have shown that players learn to play this Nash equilibrium in a series of games in which a player is matched with a different player in each period e.

Kreps et al. Our research provides further empirical tests of these theories. Our results provide additional confirming evidence and insights into why players cooperate less in an SPD game.

- Game Theory: Stochastics, Information, Strategies and Cooperation;
- 1. Introduction.
- ADVERTISEMENT.
- Game Theory - Stochastics, Information, Strategies and Cooperation | Joachim Rosenmüller | Springer!
- Navigation menu?

Bendor et al. Axelrod and Dion note that when there is uncertainty in outcomes, then cooperation may avoid unnecessary conflict but can invite exploitation. Axelrod and Donninger also presented results of tournaments of SPDs with partial feedback, finding that TFT could still perform well if there is only a small amount of noise in the payoffs.

Bendor , , Molander , and Mueller studied SPDs with partial feedback from a theoretical perspective. Our research provides further insights in this direction. To our knowledge, our experiments are the first to consider an SPD with partial feedback among live players. Furthermore, for the SPD-FF and SPD-PF games, we vary the probability of experiencing a loss so that we can decompose the direct effects of the existence of stochasticity from the magnitude value of p of the likelihood of the negative event.

Our second goal is to understand the source of any differences in cooperation between the three information conditions in terms of how players respond to different situations, which we study in Section 6.

## 6th Workshop on Stochastic Methods in Game Theory | nevacfoleana.tk

In future research, as we discuss in the concluding section, we will consider games in which there are small probabilities of loss yet high losses when they occur; risk aversion may play a more significant role in this context. The next three sections respectively characterize the nature of IDS games, our experimental design and hypotheses. To motivate our experiments in the context of interdependent security models we focus on two identical individuals, A 1 and A 2 , each maximizing her own expected value in a one-period model and having to choose whether to invest in a protective measure. Such an investment by individual i costs c and reduces the probability of experiencing a direct loss to 0.

Let p be the probability of a direct loss to an individual who does not invest in protection. That is, q is defined to be the unconditional probability of an indirect loss to the second individual when the first does not invest in protection. For example, an apartment owner who has invested in a sprinkler system to prevent fire damage may still suffer a loss indirectly from a neighboring unit that does not invest in this form of protection and experiences a fire.

The direct or indirect loss to each player is L. Let Y be the assets of each individual before she incurs any expenditures for protection or suffers any losses during the period. Assume that each individual has two choices: invest in protection, I, or do not invest, NI, and makes her decision so as to maximize expected value. The four possible expected outcomes from these decisions are depicted in Table 1.

To illustrate the nature of the expected returns consider the upper left hand box where both individuals invest in security I, I. Then each individual incurs a cost of c and faces no possible losses so that each of their net returns is Y-c. The lower left box NI, I has payoffs which are just the mirror image of these. Then each has an expected return of Y- pL - 1-p pqL.

The expected losses can be characterized in the following manner. The term pL reflects the expected cost of a direct loss. The second term reflects the expected cost from an indirect loss originating from the other individual pqL and is multiplied by 1-p to reflect the assumption that a loss can only occur once. The first constraint is exactly what one would expect if the individual could not be contaminated by the other person. Adding a second individual tightens the constraint by reflecting the possibility of contamination should this person decide not to invest in protection.

The experiments were carried out in the behavioral laboratory of a large, northeastern university using a web-based computer program. The pool of subjects recruited for the experiment consisted primarily of undergraduate students, though a small percentage of the subjects were graduate students and students from other area colleges. Between three and seven pairs of subjects participated in specific sessions. A session consisted of a set of supergames, each consisting of 10 periods. The computer program randomly paired the subjects before the start of each supergame. The number of supergames in each session ranged from three to ten depending on how long the session ran and how rapidly the pairs of players were able to complete each supergame.