Unconditional Strategies Research Articles

Evolutionary dynamics of friendship-driven reputation strategies

Indirect reciprocity refers to a cooperative mechanism in which individuals evaluate each other’s reputation and take corresponding action. It is predicated on the idea that community members frequently discuss their opinions with each other and utilize the information to determine who deserves to cooperate with. When information is disseminated publicly, all community members are able to communicate on how each other has performed in the past. We combine balanced structural relationships in social networks with reputation strategies and find that friendship-driven reputation strategies can maintain cooperation and resist the invasion of defectors. Under the condition of rare mutations, several individual decision reputation strategies based on the partners’ evaluation can enjoy higher abundances in evolutionary races. In competition with ALLD, the strategy that rely on the negative partners’ opinions is outcompeted by ALLC. The reputation strategy based on the positive partners’ opinions always maintains a very high level of cooperation even for frequent mutations. We also find that in a heterogeneous population consisting of unconditional strategies and one of the reputation strategies, a chain reaction of defection occurs. Our results highlight the significant roles of friendship-driven reputation strategies in promoting cooperation when it is challenging for individuals to observe each other’s behavior but easy for them to share information on interacting experiences of third-party members.

Direct reciprocity between individuals that use different strategy spaces.

In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on the infinitely repeated donation game and compare three natural strategy spaces: memory-1 strategies, which consider the last moves of both players, reactive strategies, which respond to the last move of the co-player, and unconditional strategies. These three strategy spaces differ in the memory capacity that is needed. We compute the long term average payoff that is achieved in a pairwise learning process. We find that smaller strategy spaces can dominate larger ones. For weak selection, unconditional players dominate both reactive and memory-1 players. For intermediate selection, reactive players dominate memory-1 players. Only for strong selection and low cost-to-benefit ratio, memory-1 players dominate the others. We observe that the supergame between strategy spaces can be a social dilemma: maximum payoff is achieved if both players explore a larger strategy space, but smaller strategy spaces dominate.

Reactive Strategies: An Inch of Memory, a Mile of Equilibria

We explore how an incremental change in complexity of strategies (“an inch of memory”) in repeated interactions influences the sets of Nash equilibrium (NE) strategy and payoff profiles. For this, we introduce the two most basic setups of repeated games, where players are allowed to use only reactive strategies for which a probability of players’ actions depends only on the opponent’s preceding move. The first game is trivial and inherits equilibria of the stage game since players have only unconditional (memory-less) Reactive Strategies (RSs); in the second one, players also have conditional stochastic RSs. This extension of the strategy sets can be understood as a result of evolution or learning that increases the complexity of strategies. For the game with conditional RSs, we characterize all possible NE profiles in stochastic RSs and find all possible symmetric games admitting these equilibria. By setting the unconditional benchmark as the least symmetric equilibrium payoff profile in memory-less RSs, we demonstrate that for most classes of symmetric stage games, infinitely many equilibria in conditional stochastic RSs (“a mile of equilibria”) Pareto dominate the benchmark. Since there is no folk theorem for RSs, Pareto improvement over the benchmark is the best one can gain with an inch of memory.

Zero-determinant strategies under observation errors in repeated games.

Zero-determinant (ZD) strategies are a novel class of strategies in the repeated prisoner's dilemma (RPD) game discovered by Press and Dyson. This strategy set enforces a linear payoff relationship between a focal player and the opponent regardless of the opponent's strategy. In the RPD game, games with discounting and observation errors represent an important generalization, because they are better able to capture real life interactions which are often noisy. However, they have not been considered in the original discovery of ZD strategies. In some preceding studies, each of them has been considered independently. Here, we analytically study the strategies that enforce linear payoff relationships in the RPD game considering both a discount factor and observation errors. As a result, we first reveal that the payoffs of two players can be represented by the form of determinants as shown by Press and Dyson even with the two factors. Then, we search for all possible strategies that enforce linear payoff relationships and find that both ZD strategies and unconditional strategies are the only strategy sets to satisfy the condition. We also show that neither Extortion nor Generous strategies, which are subsets of ZD strategies, exist when there are errors. Finally, we numerically derive the threshold values above which the subsets of ZD strategies exist. These results contribute to a deep understanding of ZD strategies in society.

Dealing with the wicked issue of child poverty: Inter‐organizational networks as forums for collective debate and reflection

AbstractIn the international realm, inter‐organizational networking is perceived as a highly relevant instrument in social policy that enables welfare organizations to deal with “wicked issues.” In this article, we discuss the central empirical findings acquired from a recent qualitative research project that focuses on inter‐organizational networks that were formed at the local level to deal with the wicked issue of child poverty as a complex and multidimensional social problem. We explore how the network discussions about normative value orientations in four inter‐organizational networks evolve, and identify three central fields of tension that illustrate the complexity for local welfare actors in and across networks to create network strategies in dealing with child poverty: (a) selective versus universal provision, (b) conditional versus unconditional strategies, and (c) instrumental versus lifeworld‐oriented approaches. Our findings show that networks can function as valuable forums for collective debate and reflection, since different approaches and perspectives to tackle the problem of child poverty can be confronted with each other. Creating such a forum has the potential to challenge dominant conceptualizations and undesirable assumptions of complex social problems that are present in welfare practices and policies.

Strategies that enforce linear payoff relationships under observation errors in Repeated Prisoner’s Dilemma game

The theory of repeated games analyzes the long-term relationship of interacting players and mathematically reveals the condition of how cooperation is achieved, which is not achieved in a one-shot game. In the repeated prisoner’s dilemma (RPD) game with no errors, zero-determinant (ZD) strategies allow a player to unilaterally set a linear relationship between the player’s own payoff and the opponent’s payoff regardless of the strategy that the opponent implements. In contrast, unconditional strategies such as ALLD and ALLC also unilaterally set a linear payoff relationship. Errors often happen between players in the real world. However, little is known about the existence of such strategies in the RPD game with errors. Here, we analytically search for all strategies that enforce a linear payoff relationship under observation errors in the RPD game. As a result, we found that, even in the case with observation errors, the only strategy sets that enforce a linear payoff relationship are either ZD strategies or unconditional strategies and that no other strategies can enforce it, which were numerically confirmed.

Nonconformity of cooperators promotes the emergence of pure altruism in tag-based multi-agent networked systems

Designing cooperation-enhancing protocols for large-scale multiagent networked systems has been a grand transdisciplinary challenge. In recent years, tag-based interactions and conformity bias have been studied extensively but separately as two viable mechanisms for cooperation enhancement in such systems. Inspired by recent studies on interaction effects in social dilemmas, we herein develop a hybrid, multiagent-based, co-evolutionary model of tag-mediated cooperation and conformity with conditional and unconditional strategies. Through a series of extensive Monte Carlo simulation experiments, we study four variants of this computational model, finding that under the majority rule, the nonconforming unconditional cooperators and conformity biased transmission of other strategies can lead to global altruistic dominance. Employing a random pinning control mechanism, we further observe that only a small fraction of nonconforming altruists is actually required to drive the system towards a robust persistence of pure altruism. Our analytic results in combination with further computational experiments reveal that spatial structure and nonconformity of cooperators are the two indispensable ingredients for the stable dominance of altruistic behavior in tag-based multiagent systems. Our findings can be beneficial for developing novel cooperation-controlling techniques in distributed self-organizing systems such as peer-to-peer networks or in various social networking and viral marketing technologies.

Welfare effects of information and rationality in portfolio decisions under parameter uncertainty

We analyse and quantify, in a financial market with parameter uncertainty and for a Constant Relative Risk Aversion investor, the utility effects of two different boundedly rational (i.e. sub-optimal) investment strategies (namely, myopic and unconditional strategies) and compare them with each other and with the utility effect of full information. We show that effects are mainly caused by full information and predictability, being the effect of learning marginal. We also investigate the saver's decision regarding whether to manage her/his portfolio personally (DIY investor) or hire, against the payment of a management fee, a professional investor and find that delegation is mainly motivated by the belief that professional advisors are, depending on investment horizon and risk aversion, either better informed (‘insiders’) or more capable of gathering and processing information, rather than possessing the ability to learn from financial data. In particular, for very short investment horizons, delegation is primarily, if not exclusively, motivated by the beliefs that professional investors are better informed.

Interplay between cooperation-enhancing mechanisms in evolutionary games with tag-mediated interactions

Cooperation is fundamental for the long-term survival of biological, social, and technological networks. Previously, mechanisms for the enhancement of cooperation, such as network reciprocity, have largely been studied in isolation and with often inconclusive findings. Here, we present an evolutionary, multiagent-based, and spatially explicit computer model to specifically address the interactive interplay between such mechanisms. We systematically investigate the effects of phenotypic diversity, network structure, and rewards on cooperative behavior emerging in a population of reproducing artificial decision makers playing tag-mediated evolutionary games. Cooperative interactions are rewarded such that both the benefits of recipients and costs of donators are affected by the reward size. The reward size is determined by the number of cooperative acts occurring within a given reward time frame. Our computational experiments reveal that small reward frames promote unconditional cooperation in populations with both low and high diversity, whereas large reward frames lead to cycles of conditional and unconditional strategies at high but not at low diversity. Moreover, an interaction between rewards and spatial structure shows that relative to small reward frames, there is a strong difference between the frequency of conditional cooperators populating rewired versus non-rewired networks when the reward frame is large. Notably, in a less diverse population, the total number of defections is comparable across different network topologies, whereas in more diverse environments defections become more frequent in a regularly structured than in a rewired, small-world network of contacts. Acknowledging the importance of such interaction effects in social dilemmas will have inevitable consequences for the future design of cooperation-enhancing protocols in large-scale, distributed, and decentralized systems such as peer-to-peer networks.

Zero-determinant strategies in finitely repeated games

Direct reciprocity is a mechanism for sustaining mutual cooperation in repeated social dilemma games, where a player would keep cooperation to avoid being retaliated by a co-player in the future. So-called zero-determinant (ZD) strategies enable a player to unilaterally set a linear relationship between the player’s own payoff and the co-player’s payoff regardless of the strategy of the co-player. In the present study, we analytically study zero-determinant strategies in finitely repeated (two-person) prisoner’s dilemma games with a general payoff matrix. Our results are as follows. First, we present the forms of solutions that extend the known results for infinitely repeated games (with a discount factor w of unity) to the case of finitely repeated games (0 < w < 1). Second, for the three most prominent ZD strategies, the equalizers, extortioners, and generous strategies, we derive the threshold value of w above which the ZD strategies exist. Third, we show that the only strategies that enforce a linear relationship between the two players’ payoffs are either the ZD strategies or unconditional strategies, where the latter independently cooperates with a fixed probability in each round of the game, proving a conjecture previously made for infinitely repeated games.

Cooperation and strategy coexistence in a tag-based multi-agent system with contingent mobility

Understanding how to enhance cooperation and coordination in distributed, open, and dynamic multiagent systems has been a grand challenge across disciplines. Knowledge employed in such systems is often limited and heuristic in nature such that cooperation-promoting mechanisms based on trust or reputation become largely unreliable. Although recent studies within the context of tag-based systems reported the emergence of stable cooperation in such uncertain environments, they were limited exclusively to only static interaction structures. Consequently, it remains unknown whether and under what conditions tag-based interactions can promote cooperation in dynamic mobile systems. We herein combine the methods of game theory, evolutionary computing, and agent-based simulation to study the emergence of tag-mediated cooperation in a mobile network with resource diversity. In a series of extensive Monte Carlo simulations, we find that tag-based interactions can give rise to high levels of cooperation even in the presence of different types of contingent mobility. Our model reveals that agent migrations within the system and the invasion of new agents from the outside can have similar effects on the evolution of dominant strategies. Interestingly enough, we observe a previously unreported coexistence of conditional and unconditional strategies in our tag-based model with costly migrations. In contrast to earlier studies, we show that this mobility-driven strategy coexistence in our model is not affected by resource limitations or other game-specific factors. Our findings highlight a striking robustness of tag-based cooperation under different mobility regimes, with important consequences for the future design of cooperation-enforcing protocols in large-scale, decentralized, and self-organizing systems such as peer-to-peer or mobile ad-hoc networks.

Predictability and Diversification Benefits of Investing in Commodity and Currency Futures

We re-examine diversification benefits of investing in commodities and currencies by considering a risk-averse investor with mean-variance preferences who exploits the possibility of predictable time variation in asset return means, variances, and covariances. We implement unconditional and conditional efficient portfolio strategies designed to exploit predictability, together with more traditional ones hitherto explored in this context (including the equally weighted, fixed weight, volatility timing, and reward-to-risk timing strategies). We find that, for all portfolio strategies, commodity and currency futures do not improve the risk-return trade-off of an investor with an existing portfolio of traditional assets (stocks and bonds), and an investment horizon of one-month. Our findings, which reverse the conclusions of previous studies that focus on static portfolio strategies, are robust across several performance metrics.

Percolation and cooperation with mobile agents: geometric and strategy clusters.

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius r(P), which accounts for the population viscosity, and an interaction radius r(int), which defines the instantaneous contact network for the game dynamics. We show that, differently from the r(P)=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.

Benefits of memory for the evolution of tag-based cooperation in structured populations

We study the effects of working memory capacity and network rewiring probability on the evolution of cooperation in the standard and modified versions of an agent-based model of tag-mediated altruism. In our evolutionary model, computational agents populate a large complex network, engage into multiplayer Prisoner’s Dilemma-like interactions, and reproduce sexually. Agents carry discernible phenotypic traits subject to mutation, memorize their own experiences, and employ different strategies when interacting with different types of co-players. Choices made are selected from a pool of two conditional and two unconditional strategies, depending on the available memory contents and phenotypic similarity among interactors. For the dominating strategy in our standard model version, we found a strong dependence of cooperation on network structure and a weak one on memory, whereas in the modified version, the structural effect was weaker than that of memory. Most importantly, we found that the previously reported decline of cooperation in memory-based models, typically observed at a high memory capacity, is now prevented with the help of tags. This suggests that the evolutionary advantages of memory capacity limits may be far more complex than previously assumed. For much smaller systems, we observed a quasi-symmetric alternation of the two winning groups of strategists. This result provides an example of ingroup biased interactions that are characterized by bursts of intra-tag cooperation interspersed with periods of unconditional transient altruism. Such switches of strategies may represent a boosting mechanism necessary for the emergence and stability of global altruism in its early evolutionary stages.

Strategy Inference in a Prisoner's Dilemma Game

We experimentally test the ability of subjects to identify repeated-game strategies from prisoner's dilemma choice data. In the experiments, subjects use a finite state grammar to build models to fit game histories. The histories are designed to distinguish between strategies with empirical and theoretical validity. We find that subjects successfully identify unconditional, punishment, and counting (or opportunistic) strategies. When data are observationally equivalent among different strategies, punishment strategies tend to be inferred. When the data are noisy, subjects' strategies overfit. The inferred strategies that do not fit the data tend to be more complex than necessary, and contain the behaviors of positive reciprocity and forgiveness, though forgiveness is not part of any relevant strategy that fits the data. Our experiment provides an empirical basis for repeated-game strategies.

The evolution of unconditional strategies via the ‘multiplier effect’

Ostensibly, it makes sense in a changeable world to condition behaviour and development on information when it is available. Nevertheless, unconditional behavioural and life history strategies are widespread. Here, we show how intergenerational effects can limit the evolutionary value of responding to reliable environmental cues, and thus favour the evolutionary persistence of otherwise paradoxical unconditional strategies. While cue-ignoring genotypes do poorly in the wrong environments, in the right environment they will leave many copies of themselves, which will themselves leave many copies, and so on, leading genotypes to accumulate in habitats in which they do well. We call this 'The Multiplier Effect'. We explore the consequences of the multiplier effect by focussing on the ecologically important phenomenon of natal philopatry. We model the environment as a large number of temporally varying breeding sites connected by natal dispersal between sites. Our aim is to identify which aspects of an environment promote the multiplier effect. We show, if sites remain connected through some background level of 'accidental' dispersal, unconditional natal philopatry can evolve even when there is density dependence (with its accompanying kin competition effects), and cues that are only mildly erroneous. Thus, the multiplier effect may underpin the evolution and maintenance of unconditional strategies such as natal philopatry in many biological systems.

Performance evaluation of dynamic trading strategies in UK stock returns incorporating lagged conditioning information

This paper evaluates the performance of the optimal mean-variance portfolio decision when lagged conditioning information is included in the investment universe. Motivated by the dynamic trading literature, we evaluate the performance of eight conditioned information portfolios against an unconditional portfolio and various benchmark strategies. We find with that including lagged conditioning information into the optimal mean-variance portfolio decision can add economic wealth. A number of the conditioning information variables used are significantly effective at improving the portfolio performance in terms of the Sharpe [1966. Mutual fund performance. Journal of Business 39, no. 2: 119–38] ratio, certainty equivalent return, and Jensen [1968. The performance of mutual funds in the period 1945–1964. Journal of Finance 23, no.2: 389–416] performance. We find that the lagged market excess returns instrument has the greatest impact on the portfolio decision.

A Risk Management Approach for Portfolio Insurance Strategies

Controlling and managing potential losses is one of the main objectives of the Risk Management. Following Ben Ameur and Prigent (2007) and Chen et al. (2008), and extending the first results by Hamidi et al. (2009) when adopting a risk management approach for defining insurance portfolio strategies, we analyze and illustrate a specific dynamic portfolio insurance strategy depending on the Value-at-Risk level of the covered portfolio on the French stock market. This dynamic approach is derived from the traditional and popular portfolio insurance strategy (Cf. Black and Jones, 1987 ; Black and Perold, 1992) : the so-called Constant Proportion Portfolio (CPPI). However, financial results produced by this strategy crucially depend upon the leverage - called the multiple - likely guaranteeing a predetermined floor value whatever the plausible market evolutions. In other words, the unconditional multiple is defined once and for all in the traditional setting. The aim of this article is to further examine an alternative to the standard CPPI method, based on the determination of a conditional multiple. In this time-varying framework, the multiple is conditionally determined in order to remain the risk exposure constant, even if it also depends upon market conditions. Furthermore, we propose to define the multiple as a function of an extended Dynamic AutoRegressive Quantile model of the Value-at-Risk (DARQ-VaR). Using a French daily stock database (CAC 40) and individual stocks in the period 1998-2008), we present the main performance and risk results of the proposed Dynamic Proportion Portfolio Insurance strategy, first on real market data and secondly on artificial bootstrapped and surrogate data. Our main conclusion strengthens the previous ones : the conditional Dynamic Strategy with Constant-risk exposure dominates most of the time the traditional Constant-asset exposure unconditional strategies.

I See What You're Doing: The Role of Gender in Cooperation

We test the impact of explicit information on individual decisions in a public goods game experiment. In the Implicit (control) condition, participants make their decisions after seeing total contributions and their own contributions. In the Explicit (treatment) condition, a different set of subjects could also see the average contribution of others in their group, which is calculated for them. Although this should not have any effect, we observe a change in behaviour across the two conditions: participants are more likely to behave as defectors or co-operators in Implicit and more likely to behave as reciprocators in Explicit. Furthermore, we find these shifts in type are almost entirely the result of differences in female behavior, i.e., more women pursuing unconditional strategies of defection or cooperation in Implicit. We interpret our findings as evidence that women are more sensitive to cues about social norms, with important policy implications.

Does mobility decrease cooperation?

We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non-contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an “always-move” rule, when compared with the strongly viscous (“never-move”) case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the problem of the onset of cooperation.