To gather data that will be used to answer the research questions posed in section 5.1 I will implement a simulation test-bed whose details will be described in this section. The decision to use a simulation was inspired by the use of simulations in every piece of research discussed in section 4.3 of chapter 4 and also by a number of researchers who were mentioned in chapter 2, especially Axelrod ([7]) and Nowak et al. ([136], [137] and [134]). The advantages of simulation are numerous, especially in the context of this thesis since simulation permits the control of all necessary game parameters and also allows the harvesting of large amounts of data in a relatively short time. It is also easier to explain observed behaviour in the context of a “real” environment than it is in a purely abstract, analytic setting. Finally, since emotions and their various facets are
inherently probabilistic, using simulations enables a wide-range of these probabilities to emerge (so long as enough repeats of a simulation are run) providing a more valid set of results and therefore conclusions to be produced.
As can be seen in section 4.3 of chapter 4, most simulations that are concerned with emotional models make use of competitive MAS games. Inspired by this, I have developed a competitive MAS simulation based upon the iterated Prisoner’s Dilemma game. The iterated version of the Prisoner’s Dilemma is a competitive, public goods game where the rational action for agents is to defect despite the chance for opponents to retaliate in subsequent rounds following a defection (see the “backward induction paradox”, discussed in section 2.1.2 of chapter 2). Since I would like to investigate how emotion can enable cooperation between agents as well as investigating how emotion affects societal interactions in general, the iterated Prisoner’s Dilemma provides a good context.
Further to this, many psychological studies designed to investigate the emergence of cooperation between human players make use of the iterated Prisoner’s Dilemma to collect data enabling their research questions to be answered (see sections 2.3, 2.4, 2.5 of chapter 2). The fact that the game has been used so frequently and so broadly by psy- chologists facilitates answering questions such as “what emotions should be modelled?” and “what are the emotion’s eliciting conditions/effects?”.
The widespread use of the game is most likely due to both the pessimistic rational prediction of the game’s outcome (see above) and because there are very few variables in the game that can influence outcomes. This ensures that any observations or results gleaned from using the game as a test-bed are relatively free from contamination by unmanaged variables. For example: players have a limited number of possible intentional actions (cooperate/defect) which makes emotion elicitation and the effects of emotion easier to model. As a consequence of these limited actions there are only four possible outcomes for each round played: CC, CD, DC, DD. Each outcome is clearly distinguished from the others so modelling emotion elicitation is again facilitated. The pay-off matrix for the Prisoner’s Dilemma is implemented in the simulation as shown in table 2.1 of section 2.1.2.
The iterated variant of the Prisoner’s Dilemma game permits me to analyse how social interactions between agents develop over a period of time. Using the standard one-shot version of the game would not yield such information rendering some of the research questions posed unanswerable. Further to this, the one-shot version of the game is not suitable since my agents require the ability to evaluate events and then modify their emotional state and intentional behaviour in light of them. Therefore, since agents need to be able to react to the actions of others and build relationships, the iterated version of the game is preferable. Using the Prisoner’s Dilemma also enables me to reuse algorithms devised by previous researchers for my simulations, reducing problems of experimental bias.
Figure 5.1: Graphical representation of player/comparator subset divisions.
5.2.1 Implementation Details
Simulations are implemented using “NetLogo” [210], further details are available in [112] and [113]. The simulation environment is a two-dimensional space and was inspired by the same common design choice employed by researchers such as Jiang et al., Bazzan and Bordini, Poel/Burghouts et al. and Zoumpoulaki et al. (see sections 4.3.5, 4.3.7, 4.3.8 and 4.3.9 of chapter 4 respectively). In these pieces of work, the simulation environment is also composed of a two-dimensional space upon which a number of agents are situated. The size of the space implemented in my own simulations varies depending upon the version of the simulation being run (details of this are provided in subsequent chapters). It should be noted that the simulation environment does not have edges except for the first version of the simulation, discussed in section 6.4 of chapter 6. If Bazzan and Bordini’s simulations in [12] are considered then the disadvantages of imposing edges become clear. Firstly, agents situated close to edges have fewer opponents than those located further away. Also, if the success of an agent is determined by its proliferation through a population then edges could dramatically affect the results obtained. For example: whilst some successful agents may propagate themselves into a maximum of eight neighbouring spaces at any one time, agents located close to edges may only be able to propagate into a maximum of five. Thus, it may be that some successful strategies are deemed unsuccessful for no other reason than they are played by agents whose propagation is spatially limited compared to other agents in the environment. This point is especially important when considering the emotions and simulation environments modelled in chapters 7 and 8.
Depending upon the simulation version used, agents may have up to two sets of opponents depending upon the simulation context. These sets are named respectively as the player and comparator sets. The player set represents the set of agents that an agent plays the Prisoner’s Dilemma against in each round. The comparator set represents the set of agents that an agent compares its score against when the comparison round is reached. The value of the comparison round is specific to particular versions of the simulation and is therefore discussed in subsequent chapters. Player and comparator sets may be further divided into four subsets: parallel, orthogonal, diagonal and octagonal sets. The agents that constitute these sets are illustrated in figure 5.1 for clarification purposes.
The blue agent in figure 5.1 denotes the agent whose player/comparator set is being described in context of. Yellow agents represent those that may comprise a parallel player/comparator set, whilst a combination of the red and yellow agents denote an orthogonal player/comparator set. Green agents illustrate the agents that comprise a diagonal player/comparator set and a combination of the yellow, red and green agents represent an octagonal player/comparator set.
The subset of agents that constitute an agent’s player and comparator sets may be different, therefore it may be the case that whilst an agent’s player set is composed of the parallel agent set, its comparator set may be composed of the orthogonal agent set. Player/comparator subsets are implemented simulation-wide i.e. it can never be the case that one agent has a player set made up of parallel agents and another has a player set composed of orthogonal agents. The same is true for comparator sets; one agent may not have a comparator set made up of parallel agents whilst another has a comparator set made up of orthogonal agents. Varying the configurations of these sets enables variations in the number of, and overlap between, the opponents played; these results are then used to compare performance of agents in different contexts.
The simulation environment houses a number of agents with different strategies or emotional characters. Agents are capable of two basic actions: cooperation or defection and mobility is restricted, no matter the particular simulation version being used. At the conclusion of each round, each agent determines its pay-off according to its own behaviour in the last round and each of their opponents. Pay-offs are calculated as per the Prisoner’s Dilemma pay-off matrix shown in table 2.1 of chapter 2.
For the simulations discussed in chapters 7 and 8 certain initial parameters for each agent present in the simulations are randomly allocated by the underlying simulation code on a per-agent basis. These initial parameters are:
An agent’s initial behaviour of i.e. does an agent cooperate or defect initially? Relevant for simulations used in chapters 7 and 8.
An agent’s initial emotional character. Relevant for simulations used in chapter 7.
Location of each agent in the simulation space. Relevant for simulations used in chapters 7 and 8.
Finally, the number of rounds to be played in any of the simulations run is never made known to any of the agents playing. This does not really matter since agents cannot do anything with this information unless they are programmed to do so, but in the interests of completeness I will make this feature of the simulations clear here.
5.2.2 Simulation Progression
The aim of this section is to make clear the general order of events that occurs in every version of the simulation implemented in this thesis. As with the size of the simulation
environment, the specifics of some steps may differ slightly for particular simulation versions but the following basic order is always adhered to:
1. All agents including the mediator are placed in the environment. These placements are pre-determined and are constant throughout the course of the simulation al- though the placing of agents is version-specific in context of the simulation.
2. Agents then choose to cooperate or defect and their action is sent to their oppo- nent(s).
3. Each agent’s emotional state and individual score is then updated accordingly (specific details for each simulation version are discussed in subsequent chapters) and if an emotion’s potential has surpassed its threshold then the agent may display the associated intentional behaviour in the next round.
4. The next round is played until the round limit is reached.
In section 2.3 the role of social interaction prior to a Prisoner’s Dilemma game, which has been explored in some of the experiments carried out with human subjects [64, 65, 162], was discussed. In the simulations run, however, no agents engage in a “con- versational phase” prior to a game beginning. Thus, no emotions are elicited before the game begins and emotions instead develop during run-time. In effect, the early rounds are a phase in which agents “get to know one another” and adopt emotional attitudes to one another, which then typically harden into stable patterns of interaction, as ex- plored in chapter 8. Because these initial turns are where agents form their emotional relationships, it could be seen as analogous to a conversational phase.