Inductive Game Theory: A Basic Scenario

The aim of this paper is to present the new theory called “inductive game theory”. A paper, published by one of the present authors with A. Matsui, discussed some part of inductive game theory in a specific game. Here, we will give a more developed discourse of the theory. The paper is written to show one entire picture of the theory: From individual raw experiences, short-term memories to long-term memories, inductive derivation of individual views, classification of such views, decision making or modification of behavior based on a view, and repercussion from the modified play in the objective game. We focus on some clear-cut cases, forgetting a lot of possible variants, but will still give a lot of results. In order to show one possible discourse as a whole, we will ask the question of how Nash equilibrium is emerging from the viewpoint of inductive game theory, and will give one answer.

Inductive Game Theory: A Simulation Study of Learning a Social Situation

Inductive game theory (IGT) aims to explore sources of beliefs of a person in his individual experiences from behaving in a social situation. It has various steps, each of which already involves a lot of different aspects. A scenario for IGT was spelled out in Kaneko-Kline (13). So far, IGT has been studied chiefly in theoretical manners, while some other papers targete

Extension from memory kits to inductively derived views

Inductive Game Theory (IGT) was developed to study the emergence of the subjective views of individuals in a social situation. In this paper we give an explicit extension process (EP) to go from a memory kit to an inductively derived view (i.d.view). We address the multiplicity problem of i.d.views by requiring a stronger link between memory threads used in the EP. We call this process a linking EP. We give a necessary and sufficient condition on the memory kit for the set of i.d.views obtained by linking EP’s to be non-empty. We give another condition for the set of i.d.views obtained to be finite. Sufficient conditions are also given directly on the objective view

The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms

The literature specifies extensive-form games in many styles, and eventually I hope to formally translate games across those styles. Toward that end, this paper defines $\mathbf{NCF}$, the category of node-and-choice forms. The category's objects are extensive forms in essentially any style, and the category's isomorphisms are made to accord with the literature's small handful of ad hoc style equivalences. Further, this paper develops two full subcategories: $\mathbf{CsqF}$ for forms whose nodes are choice-sequences, and $\mathbf{CsetF}$ for forms whose nodes are choice-sets. I show that $\mathbf{NCF}$ is "isomorphically enclosed" in $\mathbf{CsqF}$ in the sense that each $\mathbf{NCF}$ form is isomorphic to a $\mathbf{CsqF}$ form. Similarly, I show that $\mathbf{CsqF_{\tilde a}}$ is isomorphically enclosed in $\mathbf{CsetF}$ in the sense that each $\mathbf{CsqF}$ form with no-absentmindedness is isomorphic to a $\mathbf{CsetF}$ form. The converses are found to be almost immediate, and the resulting equivalences unify and simplify two ad hoc style equivalences in Kline and Luckraz 2016 and Streufert 2019. Aside from the larger agenda, this paper already makes three practical contributions. Style equivalences are made easier to derive by [1] a natural concept of isomorphic invariance and [2] the composability of isomorphic enclosures. In addition, [3] some new consequences of equivalence are systematically deduced.Comment: 43 pages, 9 figure

Evaluations of epistemic components for resolving the muddy children puzzle

We evaluate the 3 child muddy children puzzle using the epistemic logic of shallow depths GL. This system is used to evaluate what components are necessary for a resolution. These components include the basic beliefs of a child, the necessary depths of the epistemic structures, and the observations about the inactions of others added after a stage. These are all given explicitly, and their necessity is examined. We formulate the concept of a resolution as a process of inferences, actions, observations, and belief changes. We give three theorems. The first one gives a specific resolution, in which no common knowledge is involved. The second theorem states that any resolution has length of at least 3. The third theorem shows that the resolution given in the first theorem is minimal in various senses. In this manner, the necessary components for a resolution of the puzzle are evaluated

Extensive Games with Time Structures

Abstract We introduce personal time-structures and common time-structures to extensive games. These structures restrict the class of extensive games of Kuhn [8]. We show that if a player has perfect recall, then the game is personally time-structured for him. In the other direction, there are many personally time-structured games that do not satisfy perfect recall. The only known condition on memory that is required by a personally time-structured game is that no player is absent-minded. Common time-structures, on the other hand, are not related to the perfect recall condition at all. An extensive game may have perfect recall and yet no common time-structure, and conversly, a game may have a common time-structure, and no player has perfect recall. Common time-structures are used to extend backward induction results to games with imperfect recall