Yujie Zi Hawk-Dove Thesis
- 1. Zi 1 Intentions, Outcomes, and Reciprocity in Sequential Hawk-Dove Games Yujie Zi June, 2014 Dr. Michael McBride, Department of Economics Abstract Game theory models are often used to quantify human behavior. In particular, sequential Hawk-Dove games can be used to model a variety of human interactions, such as diplomacy. Hawk-Dove games are anti-coordination games in which players mutually benefit when they play different strategies in the long run. Noise is added to the Hawk-Dove games to simulate an intentions effect by randomly changing the first acting player’s decision. Two models of assessing fairness and reciprocity exist. The “process approach” theorizes that an acting player’s intentions can affect a reacting player’s payoffs. The “outcome approach” proposes that the final distributions of gains and losses affect players’ strategies. The goal of the pilot study is to generate empirical evidence to help determine whether actual outcomes, intentions, or both influence players’ decisions in Hawk-Dove game interactions. Results indicate that intentions influence decisions, but more data is needed to determine if outcomes influence decisions. Furthermore, subjects tended to make Hawk decisions.
- 2. Zi 2 Introduction The pilot study examines the effects of beliefs about others’ intentions versus others’ decision outcomes in influencing the reciprocity of either an aggressive or a passive stance. Often, reciprocity is practiced by humans through social interactions in many Hawk-Dove game scenarios, such as diplomacy. Since these interactions are usually in the form of action and reaction, and very rarely do people act simultaneously without knowing the other party’s decision outcomes, sequential Hawk-Dove games can model the interactions, instead of a standard Hawk-Dove game in which players move simultaneously. Furthermore, Hawk-Dove games are anti-coordination games, so players mutually benefit when they play different strategies. Players are severely punished for confronting each other, but gain nothing for maintaining peace with one another. Therefore, the most logical prediction of equilibria for the Hawk-Dove games would be outcomes involving players playing different strategies. Indeed, by inductive reasoning in game theory, the Nash equilibria for standard Hawk- Dove games is for one player to act as a hawk, and the other a dove. However, humans often value fairness in their actions, or follow the motto “an eye for an eye”, so in reality, the outcomes of social interactions are often peace awarded with peace, or aggression countered with aggression. Thus, by adding noise in the form of random change to determine the outcome of the first player’s decision, an intentions or inequity aversion effect could be isolated and analyzed in responding players’ behaviors. The study’s experiments measure whether actual outcomes, or intentions, or both matter to reacting players’ decisions. Furthermore, the study generates more knowledge on the dynamics of why people tend to reciprocate fairly, despite often suffering consequences in retaliating with aggression when met with aggression, and gaining little in making peace when met with peace.
- 3. Zi 3 Literature Survey Hawk-Dove games are anti-coordination games, so players tend to mutually benefit when they play different strategies. Players are punished severely for confronting each other, but gain little for maintaining peace with one another. Therefore, the logical predictions of equilibria for the Hawk-Dove games would be for players to play different strategies. By inductive reasoning in game theory, the Nash equilibria for standard Hawk-Dove games is predicted that one player acts as a hawk, while the other acts as a dove. Oprea et al. (2010) finds that in continuous Hawk- Dove games, subjects tend to reach the pure Nash Equilibrium of the game with players playing different strategies. However, Camerer (2003) produces empirical evidence that suggests that concern for reciprocity is an important factor influencing human behavior. Thus, in Hawk-Dove relatable scenarios, reciprocity could influence people to complete interactions that deviate from theory predicted anti-coordinating Hawk-Dove Nash equilibria. Two models of assessing fairness and reciprocity exist in experimental economics literature. Rabin (1993) and Dufwenberg and Kirchsteiger (2004) use a psychological game theory framework, also known as the “process approach”, derived from Geanakoplos and Pearce (1989) to model fairness. The models show that intentions are significant by suggesting that individuals’ utilities are affected by not only their own payoff, but also their belief about the goodwill of another party. Therefore, the models capture the notion that people reciprocate kindness with kindness, and hostility with hostility. The second modeling approach is the “outcome approach”, in which individuals are assumed to care mostly about the final distribution of gains and losses between themselves and other individuals so that intentions are not relevant (Fehr and Schmidt, 1999; Bolton and Ockenfels, 2000). Individuals might be willing to incur personal costs to create a more equal
- 4. Zi 4 outcome distribution so that fairness is the primary motivator behind decisions, rather than reciprocity and intentions. Many differing theoretical predictions exist in the literature so further empirical data is needed to decide which approach best models human behavior in Hawk-Dove interactions. Falk et al. (2003), Falk et al. (2008), Dhaene and Bouckaert (2010) conclude that intentions factor into reciprocity. Charness (2004) finds strong evidence for concerns about distributional outcomes along with weaker concerns for reciprocity. Bolton et al. (1998) finds little evidence for intentions significantly affecting reciprocity. Neugebauer et al. (2008) also observes little reciprocity when conducting Hawk-Dove games with economics student subjects. Ridinger (2013a) finds that both intentions and outcomes affect subjects’ decisions in prisoner’s dilemma games. Methods Participants 28 participants participated in the experiment through the Experimental Social Sciences Laboratory (ESSL) subject pool. Experimental Design The experiment uses a within and between subjects design by having participants play through multiple sequential Hawk-Dove games using computer technology in the Experimental Social Sciences Laboratory (ESSL) at UCI. The experiment is run with experimental economics software z-Tree. z-Tree is extensively used for economics experiments at the ESSL.
- 5. Zi 5 Each player, or “mover”, is randomly paired with another player and assigned as a first mover or a second mover. Individuals keep their assigned role as a first or second mover, but are matched randomly with a different partner each round. Players are given complete information about the Hawk-Dove payoffs, which translates into monetary rewards at the end of the experiment. The following payoff information was displayed to all participants: Player 1’s outcome Player 2’s outcome Payoff for player 1 Payoff for player 2 A A 1 1 A B 8 2 B A 2 8 B B 6 6 See Figure 1 in the Appendix for the hawk-dove game tree with payoffs. 1st Treatment In each round, the first mover will proceed to choose to either take the role of a hawk (aggressiveness), which will be denoted “A”, or the role of a dove (passiveness), denoted “B”. Letters “A” and “B” are used in place of the “Hawk” and “Dove” choices to eliminate “hot” language effects. In the first ten rounds, all players will be told the following information: There is a chance that the computer will change the first mover’s choice. Only the first mover’s choice may change. The second mover’s choice will never be changed. If the first mover chooses “A”, then there is a 50% chance that the computer will change the first mover’s choice to “B”. If the first mover chooses “B”, then no changes will occur. 2nd Treatment In the last ten rounds, all subjects will be told that if the first player chooses “A”, then there is a 10% chance that the computer will change the first mover’s choice to “B”. If the first mover chooses “B”, then no changes will occur. After the first mover moves, the second mover will then decide to choose “A” or “B”.
- 6. Zi 6 Treatment 1 was run first, followed by treatment 2. Not enough funding was obtained to run a reversed order session to eliminate ordering effects, although we intend to do so in the future. At the end of each round, both players’ moves were matched and the resulting payoffs were calculated. Subjects also completed a survey containing questions on demographics and opinions on empathy, social preferences, and concerns for fairness. At the end of the experiment, payoffs were tallied and converted to monetary rewards to be given to the subjects. All subjects received a $7 show-up compensation and additional monetary rewards calculated through randomly choosing the payoff obtained in one of the rounds. Results The data shows that subjects are more likely to display Hawk tendencies in Hawk-Dove sequential games. In the first treatment, an average of 67% of first movers chose A (Hawk). In the second treatment, an average of 83% of first movers chose A (Hawk). In the first treatment, an average of 61% of second movers chose A (Hawk). In the second treatment, an average of 46% of second movers chose A (Hawk). Across all rounds, AB (Hawk-Dove) was the most common outcome. BB (Dove-Dove) was the least common outcome. The proportion of first mover A (Hawk) choices increased, and the proportion of second mover A (Hawk) choices decreased as the experiment progressed, resulting in more AB (Hawk-Dove) outcomes. Outcomes were headed towards an anti-coordination equilibrium, as consistent with Nash equilibrium theory. When the first mover chose A (Hawk) and the computer did not change the choice, around 40% of second movers reciprocated with a Hawk choice, resulting in both movers
- 7. Zi 7 earning the payoff of $1, despite sacrificing a higher payoff with a Dove choice with the second mover earning $2, while the first mover would earn $8. When the first mover chose A (Hawk) and the computer reversed the first mover’s choice to B (Dove), also denoted as a Hawk- intended Dove outcome, the second mover responded with a choice of A (Hawk) over 90% of the time. However, the amount of data points generated were too few for first mover Hawk- intended Dove outcomes, so the proportion of subjects who had Hawk intentions and ended with Dove choice outcomes could not be compared to Dove choices, which would test for an outcomes effect. Refer to Figures 2 and 3 in the Appendix to observe second mover hawk responses to first mover choices across all periods. Microsoft Excel and SAS were used to analyze the data. Discussion The data supports that a process approach, or an intentions effect, is in effect due to the high proportion of second movers responding to first mover hawk-intended dove outcomes with hawk choices. In Figure 2 and 3, the average second mover hawk choices in response to hawk- intended computer chosen dove outcomes (green line) is consistently higher than the average second mover hawk choices in response to first mover dove choices (red line), suggesting that people do care about intentions, if the outcomes of the first mover’s decisions are the same. More Dove-Dove equilibria were expected, but as the experiment progressed, subjects tended to anti-coordinate resulting in Hawk-Dove equilibria. The majority of second movers are not rewarding first movers for their dove choices with a dove response because the second movers are trying to maximize their payoffs and disregard good first mover intentions, instead of
- 8. Zi 8 sufficing with a mediocre payoff of $6. Intentions do matter, but subjects do not always reward good intentions with good reciprocity. Differences in behavior between first treatment and second treatment suggests there may be an outcomes effect, but we cannot conclude that there is an outcomes effect due to the lack of data examining the reaction of second movers to first mover hawk-intended dove results. More data from a reverse treatment session is needed to correct for ordering effects to make conclusions. Furthermore, some Dove-Dove outcomes occurred so there could be an outcome effect due to the fact that even though second movers saw that the first mover was trying to exhibit hawk behavior, second movers still decided to choose dove, instead of being spiteful and choosing hawk, which would have earned the second movers a higher payoff of $2 as compared to $1. This could suggest that second movers care about the Pareto efficient outcome or have a preference for equality, suggesting effects of an outcome approach. Insufficient first mover hawk-intended dove outcome data points were generated to test for significance for an outcomes effect, so any linear regressions are void until further data is generated. Conclusion Intention effects affect subjects’ decision in Hawk-Dove games, but outcomes’ effects remain inconclusive, although there is a possibility that an outcomes effect could also exist. Subjects tended to exhibit Hawk behavior, but the Nash equilibria of anti-coordination decisions were still predominant throughout the experiment. Several pieces of literature study outcomes, but the study of the process approach is much more limited, and this pilot study provides more conclusive evidence about process approach effects.
- 9. Zi 9 Since the experiment is a pilot study, with more funding, a session can be run to eliminate potential ordering effects by reversing treatments. An increase in the probability of a random choice reversal for the second treatment could also help generate more noise to produce more data for Hawk-intended Dove choices. Future experiments could also include adding noise to only the Dove choice, or framing the experiment to give context to Hawk-Dove interactions with intentions, such as simulations in investing in nuclear weapons research. With more framing, the experiment could be extended to simulate political interactions such as diplomacy, or financial interactions such as competitive markets.
- 10. Zi 10 Acknowledgements I would like to express my sincerest gratitude to Professor McBride for allowing me to use the ESSL facility for my experiment and for his guidance, encouragement, and teaching in conducting experimental economics research. I would also like to thank Garret Ridinger for his company and his help with grant writing, experimental design, programming, and data analysis. My gratitude is also extended to my former mentor, Boris Wong, for introducing me to the field of experimental economics and encouraging me to conduct research. Finally, I would like to thank my parents for continually supporting me throughout my studies.
- 11. Zi 11 References Bolton, G. E., Brandts, J., Okenfels, A., 1998. “Measuring motivations for the reciprocal response observed in a simple dilemma game.” Experimental Economics 1 (3), 207–219. Bolton, G. E., Okenfels, A., March 2000. “Erc: A theory of equity, reciprocity, and competition.” The American Economic Review 90 (1), 166–193. Camerer, C. F., 2003. “Behavioral Game Theory: Experiments in Strategic Interaction.” Princeton University Press. Charness, G., July 2004. “Attribution and reciprocity in an experimental labor market.” Journal of Labor Economics 22 (3), 665–688. Dhaene, G., Bouckaert, J., 2010. “Sequential reciprocity in two-player, two-stage games: An experimental analysis.” Games and Economic Behavior 70, 289–303. Dufwenberg, M., Kirchsteiger, G., 2004. “A theory of sequential reciprocity.” Games and Economic Behavior 47, 268–298. Falk, A., Fehr, E., Fischbacher, U., January 2003. “On the nature of fair behavior.” Economic Inquiry 41 (1), 20–26. Falk, A., Fehr, E., Fischbacher, U., 2008. “Testing theories of fairness - intentions matter.” Games and Economic Behavior 62, 287–303. Fehr, E., Schmidt, K. M., August 1999. “A theory of fairness, competition and cooperation.” The Quarterly Journal of Economics 114 (3), 817–868.
- 12. Zi 12 Fischbacher, Urs., 2007. “z-Tree: Zurich Toolbox for Ready-made Economic Experiments.” Experimental Economics 10 (2), 171-178. Geanakoplos, J., Pearce, D., 1989. “Psychological games and sequential rationality.” Games and Economic Behavior 1, 60–79. Neugebauer, T., Anders P., and Arthur S., 2008. “Fairness and Reciprocity in the Hawk–Dove Game.” Journal of Economic Behavior & Organization 66 (2), 243–250. Oprea, R., Henwood, K., Friedman, D., July 2010. “Separating the Hawks from the Doves: Evidence from Continuous Time Laboratory Games.” Journal of Economic Theory, Elsevier, 146 (6), 2206–2225. Rabin, M., 1993. “Incorporating fairness into game theory and economics.” The American Economic Review 83, 1281–1302. Ridinger, G., 2013a. “Control, reciprocity, and inequity aversion in a sequential prisoner’s dilemma with nature.” Working Paper.
- 13. Zi 13 Appendix Figure 1 – Hawk-Dove game tree Figure 2 – Second mover hawk responses for periods 1 to 10 (c=.5)
- 14. Zi 14 Figure 3 – Second mover hawk responses for periods 11 to 20 (c=.1)