Justified Communication Equilibrium

Justified communication equilibrium (JCE) is an equilibrium refinement for signaling games with cheap-talk communication. A strategy profile must be a JCE to be a stable outcome of nonequilibrium learning when receivers are initially trusting and senders play many more times than receivers. In the learning model, the counterfactual “speeches” that have been informally used to motivate past refinements are messages that are actually sent. Stable profiles need not be perfect Bayesian equilibria, so JCE sometimes preserves equilibria that existing refinements eliminate. Despite this, it resembles the earlier refinements D1 and NWBR, and it coincides with them in co-monotonic signaling games. (JEL C70, D82, D83, J23, M51)

A Biform Game Model with the Shapley Allocation Functions

We define the mixed strategy form of the characteristic function of the biform games and build the Shapley allocation function (SAF) on each mixed strategy profile in the second stage of the biform games. SAF provides a more detailed and accurate picture of the fairness of the strategic contribution and reflects the degree of the players’ further choices of strategies. SAF can guarantee the existence of Nash equilibrium in the first stage of the non-cooperative games. The existence and uniqueness of SAF on each mixed strategy profile overcome the defect that the core may be an empty set and provide a fair allocation method when the core element is not unique. Moreover, SAF can be used as an important reference or substitute for the core with the confidence index.

Legitimate equilibrium

We present a general existence result for a type of equilibrium in normal-form games, which extends the concept of Nash equilibrium. We consider nonzero-sum normal-form games with an arbitrary number of players and arbitrary action spaces. We impose merely one condition: the payoff function of each player is bounded. We allow players to use finitely additive probability measures as mixed strategies. Since we do not assume any measurability conditions, for a given strategy profile the expected payoff is generally not uniquely defined, and integration theory only provides an upper bound, the upper integral, and a lower bound, the lower integral. A strategy profile is called a legitimate equilibrium if each player evaluates this profile by the upper integral, and each player evaluates all his possible deviations by the lower integral. We show that a legitimate equilibrium always exists. Our equilibrium concept and existence result are motivated by Vasquez (2017), who defines a conceptually related equilibrium notion, and shows its existence under the conditions of finitely many players, separable metric action spaces and bounded Borel measurable payoff functions. Our proof borrows several ideas from (Vasquez (2017)), but is more direct as it does not make use of countably additive representations of finitely additive measures by (Yosida and Hewitt (1952)).

On selecting the right agent

Each period, a principal must assign one of two agents to a new task. Each agent privately learns whether he is qualified for the task. An agent wishes to be chosen independently of qualification and chooses whether to apply for the task. The principal wishes to appoint the most qualified agent and chooses which agent to assign as a function of the public history of profits. We fully characterize when the principal's first‐best payoff is attainable in equilibrium and identify a simple strategy profile achieving this first‐best whenever feasible. Additionally, we provide a partial characterization of the case with many agents and discuss how our analysis extends to other variations of the game.

Distance-Based Equilibria in Normal-Form Games

We propose a simple uncertainty modification for the agent model in normal-form games; at any given strategy profile, the agent can access only a set of “possible profiles” that are within a certain distance from the actual action profile. We investigate the various instantiations in which the agent chooses her strategy using well-known rationales e.g., considering the worst case, or trying to minimize the regret, to cope with such uncertainty. Any such modification in the behavioral model naturally induces a corresponding notion of equilibrium; a distance-based equilibrium. We characterize the relationships between the various equilibria, and also their connections to well-known existing solution concepts such as Trembling-hand perfection. Furthermore, we deliver existence results, and show that for some class of games, such solution concepts can actually lead to better outcomes.

A simple model of production and trade in an oligopolistic market: back to basics

We provide a two good model of oligopolistic production and trade with one good being commodity money. There is the usual demand function of the consumers for the produced good that producer-sellers face. Each seller is a budget constrained preference maximizer and derives utility (or satisfaction) from consuming bundles comprising commodity money and the produced good. We define a competitive equilibrium strategy profile and a Cournotian equilibrium and show that under our assumptions both exist. We further show that at a competitive equilibrium strategy profile, each seller maximizes profits given his own consumption of the produced good and the price of the produced good, the latter being determined by the inverse demand function. Similarly we show that at a Cournotian the sellers are at a Cournot equilibrium given their own consumption of the produced good. Assuming sufficient differentiability of the cost functions we show that at a competitive equilibrium each seller either sets price equal to marginal cost or exhausts his capacity of production; at a Cournotian equilibrium each seller either sets marginal revenue equal to marginal cost or exhausts his capacity of production. We also study the evolution of Cournotian strategies as the sellers and buyers are replicated. As the number of buyers and sellers go to infinity any sequence of interior symmetric Cournotian equilibrium strategies admits a convergent subsequence, which converges to an interior symmetric competitive equilibrium strategy. In a final section we discuss the Bertrand Edgeworth price setting game and show that a Bertrand Edgeworth equilibrium must be a derived from a competitive equilibrium price. Here we show that if at a symmetric competitive equilibrium, the sellers consume positive quantities of the produced good then the competitive equilibrium cannot be a Bertrand Edgeworth equilibrium. Thus, if at all symmetric competitive equilibria the sellers consume positive amounts of the produced good, then a Bertrand Edgeworth equilibrium simply does not exist.

Critical Reading Skills at Tertiary Level

This study investigated critical reading skills among tertiary level students. Ten undergraduate students from the Faculty of Science, Universiti Teknologi Malaysia (UTM) participated in this research. They were required to read a text regarding an oil crisis and respond to a question given in a form of a written protocol. A Critical Reading Categorization Scheme, adapted from the strategy profile developed by Sugirin’s (1999) was used to analyse the written protocol data. It was found that a number of sub-skills were used by the students, among them which were consistently used include extracting information from reading text, using examples to support argument, stating opinion regarding the topic discussed, stating personal viewpoint on the issue discussed and providing explanations for opinion stated. Overall, the results showed that the students were able to moderately respond critically to the text they read.

An Algorithm for Computing All Berge Equilibria

An algorithm is presented in this note for determining all Berge equilibria for an n-person game in normal form. This algorithm is based on the notion of disappointment, with the payoff matrix (PM) being transformed into a disappointment matrix (DM). The DM has the property that a pure strategy profile of the PM is a BE if and only if (0,…,0) is the corresponding entry of the DM. Furthermore, any (0,…,0) entry of the DM is also a more restrictive Berge-Vaisman equilibrium if and only if each player’s BE payoff is at least as large as the player’s maximin security level.