**Chapter 4** Games and Social Reality

*Yasuo Nakayama*

### **Abstract**

In this chapter, I will show that social activities can be seen as activities in games. In Section 2, rested on a formal framework called Dynamic Belief-Desire-Obligation Logic, I propose a model of agents who can play games. In Section 3, based on this framework, a rule system of a game is interpreted as a normative system that determines the obligation space and the permission space of each player. In a game stage, each player fulfills her obligations and chooses an action type from their permission space and performs it. These actions change the state of the game and determine new obligation and permission spaces of all participating players. In Section 4, I interpret social actions as actions based on normative systems. Social normative systems determine obligation and permission spaces of members of a social organization and restrict their activities. In Appendix, formal systems mentioned in this chapter are described in detail.

**Keywords:** normative system, dynamic belief-desire-obligation logic, philosophy of action, social ontology, actions in games, speech acts, role-specific normative spaces

#### **1. Introduction**

This chapter deals with some problems in social ontology. I investigate the following questions. How can we characterize agents who constitute social organizations? How is the society structured? How is the social reality created? To the first question, I answer that agents who can play team games constitute social organizations. It is my proposal to the second question that role-specific normative requirements structure social organizations. The social reality is created by agents who perform actions respecting socially accepted normative systems. This is my answer to the third question. These activities of agents can be explained by analyzing agents who play team games. We can observe that many games are clearly structured. Thus, investigations on games may contribute to analysis of the social reality.

In philosophy of action, Donald Davidson proposed to reduce intention to desire and means-end-belief [1]. Michael Bratman opposed to this claim and interpreted intention as planning [2]. Furthermore, against reductionistic approach, John Searle pointed out that some actions are strongly influenced by deontic requirements [3]. To this problem, this chapter proposes a new alternative position. Namely, I suggest taking beliefs, desires, and normative beliefs as mental bases for planning and decision-making. Some actions are temporally extended and include substructural actions. A series of actions in a game is an example of such temporally extended

actions. In this chapter, I will show how beliefs, desires, and normative beliefs are connected to realize the leading desire in the given constraints.

There are three major logical approaches to investigations on dynamic inferences, namely dynamic epistemic logic [4, 5], logic of belief revision [6, 7], and discourse representation theory [8, 9]. My formal approach in this chapter is mainly related to the last two approaches. The formal details of the framework in this chapter can be found in Appendix.

For the sake of space, I do not discuss collective actions in this chapter (for collective actions, see [10]). However, the model proposed in this chapter can be also applied to characterizations of collective actions.

#### **2. Model of agents**

A game is played by agents who perform actions keeping the rule system of the game. All participating agents respect the rule system of the game when they play it. Otherwise, the game will be broken down. Then, what kind of features are required for agents who can play games? This is the leading question of this section.

A rule system of a game can be interpreted as a normative system [11]. I proposed in some articles to represent a normative system by a pair hBB, OBi constituted of a belief base BB and an obligation base OB [11, 12]. A player masters this normative system and decides her action based on it. Furthermore, her decision of the next action is influenced by her desire of winning the game. In each game stage, a player will perform an action type that is considered as a promising move to win the game. Here, I take a desire base DB into consideration and define Belief-Desire-Obligation system hBB, DB, OBi as follows [13, 14].

#### **2.1 (S2.1) Belief-Desire-Obligation system (BDO-system)**


f. We call socially accepted BO-system normative system.

Normative systems such as laws can be expressed as BO-systems [12]. In Section 3, we will see that a rule system of a game can be interpreted as a normative system.

Note that the definition of BDO-system in (S2.1) allows conflicts between the BD-system and the BO-system. This feature reflects cases in which an agent has a desire that conflicts with her BO-system. When an agent prefers her desire even if this desire conflicts with an accepted normative system, a performance of a prohibited action becomes possible.

Now, we can introduce some logical operators and define a logical framework Belief-Desire-Obligation Logic (BDO-Logic) (for details, see Appendix (Ap.1)). For agent A, logical operators in BDO-Logic are BA, MA, OA, FA, PA, and DA. The intended meaning of sentences with these operators can be expressed as follows: A believes φ (BA φ), A believes that possibly φ (MA φ), A believes it is obligated φ (OA φ), A believes it is forbidden φ (FA φ), A believes it is permitted φ (PA φ), and A believes it is desired φ (DA φ). The following list describes some important features of these operators.
