**Question 1 [a] **

*Considering relevant theoretical models, evaluate the core ideas of Bayesian persuasion and loss aversion.*

Loss aversion is a decision principle that has a natural preference of profit to loss when it comes to economic dynamic and decision making. This decision is supported by some paradigms that affirm that the prospect theory entirely explains loss aversion. It means that loss aversion is all about making deliberate choices based on a particular relative reference point rather than getting concern on the ideal outcome. This ideology is driven by the probability of loss and gain that is obtained in business dealings. According to Kahneman & Tversky (2013), the choice of gaining or losing is dependent on the lesson one learns from either of the two. Primarily, they affirm that the pain experienced when one loss is psychologically about double as much power as the pleasure experienced in gaining.

The utterly need that is loss aversion driven explain different kinds of business cultures. For instance, in the case where a person owns a company that produces pens, he is bound to praise his brand of pens for profit gains. This kind of behavior is identified as the endowment effect. Loss aversion contributes significantly to the endowment effect as no one would wish to experience loss. That becomes their loss aversion technique. On the same note, loss aversion can lead to sunk cost fallacy. It is where an individual will continue scheduling her time in an ongoing business driven by the amount of time, commitment and investments she has made before on the same company.

Bayesian persuasion can be simplified as the ability of an individual to persuade another to change her action/s with the help of a persuasion mechanism. For instance, in the case where a sender would attempt to influence a receiver, there is a good deal of command for a sizeable share of resources that will be beneficial for either or both of the two. This kind of persuasion plays a vital role in significant business activities that would include advertising, financial disclosure among others. Several different possible persuasion outcomes are driven by the interest of the sender and the receiver. Each of the possible results is standardized to the probability of the findings themselves. In such a condition of persuasion between the sender and the receiver, the prior belief of the possible outcome usually forms a chance of 0.3 [P(0.3)]. At the end of it all, a sender can change the receiver’s action only by changing the receiver’s belief.

**Question 1 [b]**

*Complete these ideas with your example of Bayesian persuasion and your example of loss aversion.*

**Bayesian persuasion** – In an instance where a prosecutor is involved in a case in court, he is expected to persuade the judge that the case before her requires a conviction. Until then, the judge has the right to think otherwise and acquit for lack of convincing evidence that proves that the defendant is guilty. In this case, the prosecutor is the sender, and the judge is the receiver.

Let the option of acquit be ** i** and convict be

The state of the outcome of the case before the receiver will depend on the position that the sender takes in approach to persuade the receiver to convict. In the fact where the Sender’s payoff takes a concave approach to the Receiver’s default idea, there is no disclosure of information that is needed. On the same note, if the Sender’s payoff takes a convex approach to that of the Receiver’s default idea, there is a need for full disclosure of information. See figure 1 below:

Illustration 1: Concave Closure Illustration

The prosecutor would plan to increase his payoff by decreasing P(*i*) and increasing P(*g*). It would increase the probability of *g* and thus would increase the likelihood of the judge (receiver) to be willing to convict. The actions outlined above are explained by optimal mechanism and aid in a general conclusion that the moment Receiver takes the Sender’s least preferred action, she is confident that the state is where the outcome is optimal. See Illustration 2 below:

Illustration 2: Motivating Example

**Loss aversion** – There are different ways through which loss can be avoided for the hope of gaining. Most of the approaches that are used are determined to directly positivity to enhance gains. As already outlined herein, when the loss is averted by endorsing directly for gaining purpose, then endowment effect or the sunk cost fallacy is likely to dominate decision making.

A real-life situation that loss aversion is applied is where it is used to allow people to commit to a positive change of behavior. The Department of Public health and social welfare can take the approach of exposing the negative impacts of something to discourage people from using such things in their day-to-day lives. This approach supports Gatcher’s et al. (2010) idea that sometimes penalty frames are greater motivators of people than reward frames. In the example above, the relevant authorities may be prompted to create awareness for people to give up junk food or face cash penalty in the case of non-compliance. The principle of fear of loss will increase the number of people who comply with such notice against junk foods. This illustration is an indication of loss aversion.

**Question 1 [c]**

*Examine how the canonical model of Bayesian persuasion can be adapted to include loss aversion and provide an intuition for what additional aspect of the real world loss aversion seeks to capture in this framework.*

Persuasion is essential in any decision-making mechanism especially when it comes to deciding loss aversion. Bayesian persuasion in itself entails the cognitive indulging of a candidate distribution of posterior that is encouraged by a persuasion mechanism. It is the basic expectation where the sender is expected to persuade and change the actions of the receiver. More importantly, other underlying factors are involved in the analysis of the common interest of individuals who take part in the persuasion process. The context of persuasion and the involvement of ideologies of belief are essential indicators of the kind of relationship the sender and the receiver have when it comes to who will benefit from the persuasion process.

According to Gentzkow & Kamenica (2015), the concept of language multiplier takes a course in the case where Bayesian persuasion adapts loss aversion in the decision-making mechanism. The Lagrangian multiplier is interpreted as the price for posterior for sufficient conditions that ensure optimality. In this case, both the concept of persuasion and loss aversion take part in the decision-making process and the result obtained is the optimal outcome possible. Therefore, in the case of an optimal solution, a Lagrangian multiplier exists rationalizing it.

Taking an instance where a school principal is overseeing a construction project in the school, and he hires a contractor to engage in the project implementation. Where the principal tries to persuade the contractor to exert costly effort to complete the construction project, the contractor receives a reward for a fraction of the value of the project, but it is the principal who knows the actual cost of the project. In the case where the value of the project is low, the principal should disclose it and make great realization pooled into a single signal.

Duality is applied in Bayesian persuasion where two or three actions are options for the receiver to choose from (See figure 3 below). It means that the receiver cannot consider avoiding any of the available choices. The standard option provided is an indication of the fact that the decisions are made available and the receiver has the task of identifying which of those has merit. Kolotilin (2015) explains that the persuasion made by the sender drives the decision. In this case, the objective function of the sender is almost arbitrary. This condition allows for a continuum of both actions and states.

Figure 3: Two-Action Case

**Question 1 [d]**

*Compare and contrast the predictions of the standard model of Bayesian persuasion with the modified model that incorporates loss aversion.*

**Similarities**: (i) The standard model of Bayesian persuasion is all about making the receiver change her actions based on the persuasion approach by the sender. The modified model of Bayesian persuasion is also about persuading a receiver to choose activities that are already known to both the sender and the receiver.

(ii) The possible outcome of belief in the standard model of Bayesian persuasion is standardized to the probability of the issue. Similarly, the result obtained in the modified model of Bayesian persuasion adapted to loss aversion is determined by an optimal signal.

(iii) In a standard model of Bayesian persuasion, there is a sizeable share of resources for both the sender and the receiver during the outcome of a belief. On the same note, a modified model of Bayesian persuasion and loss aversion provide a discrete benefit to either the sender or the receiver based on the disclosure of information.

**Differences**: (i) In the standard model of Bayesian Persuasion, the decision making process is all about merit and persuasion of the Sender to the Receiver to change her actions. , in this case, is when the Receiver changes her mind. On the other hand, the modified model of Bayesian Persuasion adapted to loss aversion, the concern in decision making is the least loss experience or total loss avoidance option. In the first case, the sender and the receiver benefit from Sender’s payoff. In the second case, the Sender may not benefit from the decision making process.

(ii) The standard model of Bayesian Persuasion may involve two approaches of the Sender to the Receiver – concave or convex approaches. In these two approaches, the most critical consideration is that the decision-making process assumes an optimal mechanism. In the modified model of Bayesian persuasion adapting loss aversion, the method of decision making is similar (optimal solution), but in this case, the Lagrangian multiplier exists for rationalizing the answer.

(iii) The standard model for Bayesian persuasion takes two approaches, either positive or negative; which would also mean the receiver would accept to change her mind or reject. The outcome will depend on the Sender’s payoffs to persuade. On the other hand, the modified model of Bayesian persuasion adapting to loss aversion, the Receiver’s approach is one – accepting to change her action. What is different is that in this case, there are different choices available to which the receiver has to choose from which of them is the best option. It allows for the continuum of the states and actions.

**References**

Gächter, S., Herrmann, B., & Thöni, C. (2010): Culture and cooperation. *Philosophical Transactions of the Royal Society B: Biological Sciences*, *365*(1553), 2651-2661.

Gentzkow, M., & Kamenica, E. (2015): Information environments and the impact of competition on information provision. *University of Chicago mimeo*.

Kahneman, D., & Tversky, A. (2013): Choices, values, and frames. In *Handbook of the Fundamentals of Financial Decision Making: Part I* (pp. 269-278).

Kolotilin, A. (2015): Experimental design to persuade. *Games and Economic Behavior*, *90*, 215-226.