EXTENDED ABSTRACT (To access pdf file please click on the title above or git link to PDF (for google drive link, if does not load please click download))In this paper, I explore privately informed agents' incentives to induce public polarization for their own gain. In order to discipline the exercise, I assume that the audience being polarized is rational and processes all new information using Bayes' rule. I start with the pure cheap talk communication game of (Crawford and Sobel 1982) and add a second receiver to make belief polarization meaningful. Specifically, the sender must choose one costless but unverifiable message, publicly observed by both receivers. After observing this common signal, the receiver's update their beliefs according to Bayes' rule, and then each takes a separate action. The sender's payoff depends on the average action taken, and the state-contingent preferences of the sender and each receiver are not fully aligned. In contrast, the receiver's have identical state-contingent preferences.

To allow rational belief polarization, I use the approach used in (Benoit and Dubra 2019). I assume that the state space is two dimensional.  The payoff relevant dimension is a scalar that directly enters the payoff function for all agents. The payoff- irrelevant dimension is a binary variable that does not directly enter any payoff functions but nonetheless may affect posterior beliefs. Receivers agree on the prior distribution of the payoff relevant variable, but their beliefs about the payoff irrelevant variable are different. Receivers in my model are rational but have different beliefs.

To avoid contradicting the disagreement theorem in (Aumann 1976), I assume that agents agree to disagree. Formally receiver 1 does not update his belief based on the prior of receiver 2 and vice versa. I assume that receivers rationally process all new information, despite the initial disagreement.

Suppose the sender employs a one-dimensional partition; namely, she either fully reveals the payoff irrelevant state or does not reveal any additional information about this binary variable. The set of equilibria with one-dimensional partitions in the current model is payoff equivalent to the set of equilibria in the standard cheap talk model. However, allowing for the payoff irrelevant dimension introduces a continuum of new equilibria and expands the set of equilibrium payoffs.

I characterize a set of polar equilibria and prove that this set of equilibria spans the sender's payoff space. I also show that in these equilibria, receivers are polarized. Namely, their posterior beliefs are ordered with first-order stochastic dominance. Moreover, I show that when ex-ante receivers disagreement rises, then there is more scope for manipulation by the sender. Specifically, the set of aggregate actions (and thus sender payoffs) that can be supported in equilibrium expands as the receivers' posterior beliefs diverge. I show that even slight disagreement about payoff irrelevant state is enough for influential equilibrium to exist for any bias level. When disagreement increases, the equilibria set expands, and the bias threshold above which there are no informative equilibria also increases.

EXTENDED ABSTRACT (To access pdf file please click on the title above or git link to PDF (for google drive link, if does not load please click download))

This paper considers a Bayesian persuasion game between a single sender and two receivers. The sender's payoff is monotone in the receivers' beliefs about the payoff relevant state. All agents share a common prior about this state. However, we allow disagreement about a payoff irrelevant state, a binary variable that enters no utility functions. When all agents have the same prior beliefs about payoff irrelevant state, then the model is a version of Kamenica and Gentzkow (2011). However disparate priors significantly change the results. In particular, it is no longer true that sender fully conceals the state when her payoff is concave in beliefs and fully reveals the state when payoff is convex in beliefs. In fact, if the sender's payoff is differentiable and strictly monotone, then even slight disagreement on the payoff irrelevant state guarantees that the sender can strictly increase her payoff by using an informative signal. Moreover, the sender's payoff is strictly increasing in the prior disagreement between the receivers. Given extreme prior disagreement between the receivers, we show that per-suasion induces significant belief polarization for two general classes of payoff functions. Specifically, if the sender's payoff is biconcave and submodular, then signals are strongly polarizing; namely, the signal that makes receiver 1 most confident that the payoff relevant state is 1 makes receiver 2 least confident that the payoff relevant state is 1, and the signal that makes receiver 1 second most confident the payoff relevant state is 1 makes receiver 2 second most confident the payoff relevant state is 1, etc. If the sender's payoff biconvex, then the sender chooses a message service with three signals, and receiver's beliefs are diametrically opposed for two of the three signals.

In this paper,  I  extend the Gale and Shapley algorithm for the standard marriage market model. In my extension, a set of agents who make offers is a mixed set of men and women. Resulted matching is not necessarily stable. However, every stable matching is either result of extended Gale and Shapley algorithm applied on some mixed set of agents or could be represented as join or meet of stable matchings, which are results of the extended algorithm.

This is my master's thesis, which I wrote for my master studies  in Computational Logic
ABSTRACT
(To access pdf file please click on the title above or git link to PDF (for google drive link, if does not load please click download))

In this master thesis, we have determined the minimal extension of quantified propositional Lukasiewicz logic, which admits quantifier elimination. To obtain this result, we solved the following problems: we have extended Lukasiewicz logic by all division operators and have proven completeness of the extended logic. Afterward, we used McNaughton theorem to determine the so-called minimax points of Lukasiewicz logic truth functions. We expressed these points in the language of Lukasiewicz logic extended by all division operators, then by combining the results mentioned above, we have obtained the desired admissibility quantifier elimination. As a corollary, we obtained that quantified propositional Lukasiewicz logic extended by all division operators is semantically complete, decidable, and hence recursively enumerable.