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Rachel E. Kranton on Network Models - Dictionary of Arguments

Kranton I 425
Network Model/Communication/Bloch/Demange/Kranton: In the “network communication model”, agents are organized along a social network.
Kranton I 426
The “network model” represents an environment where individuals communicate privately to colleagues or friends, such as in texts, e-mails, and phone calls. People know each others’ types and can pass on information, but again the original source of the information is unknown (…).
>Public Broadcasting/Kranton
Kranton I 427
Differences of the network model in contrast to the public broadcast model:
1. Agents communicate pairwise.
2. Agents’ types are common knowledge.
The combination of these two features can allow communication even when no truthful communication is possible in public broadcast. With pairwise transmission of messages and knowledge of where agents of different types are located, agents can judge the veracity of a message transmitted through a particular part of the network and block it from reaching others. This blocking then increases the veracity of other messages that then circulate.
In the network model a pair of agents i and j have a link, denoted by ij, if they have the potential to communicate, and we say agent i is agent j ’s neighbor and vice versa. Although the underlying structure of the social network is undirected, communication could occur in either, both, or neither direction. To indicate the direction of any communication, let (i, j ) denote the directed link from i to j, (j, i) denote the directed link from j to i, and let G denote the set of all directed links. G and individual agents’ types are common knowledge. We assume that the network is connected; that is, every agent has at least one neighbor. (…) agents are connected in such a way that a message can reach any individual through only one route.
Equilibrium/Network Model: an equilibrium in the network model consists of message creation strategies, transmission strategies, and beliefs (Mi, ti, ρi) for each agent i such that each agent’s strategy is sequentially rational given the beliefs and strategies of others, and beliefs are formed using Bayes’ rule from the strategies whenever possible. >Communication Equilibria/Bayesianism, >Communication Activity/Kranton.
Kranton I 434
Agent Replacement/Agents/Networks/Bloch/Demange/Kranton: We perform a comparative static exercise on the number of biased agents; we replace one biased agent with one unbiased agent and consider the effect of this replacement on individual welfare. The replacement of an unbiased agent by a biased agent j decreases the utility of unbiased agents but could increase or decrease the expected utility of biased agents. There are three effects (…):
1. a direct effect on the number of votes for collective action 1,
2. a direct effect on information transmission because a message m = 1 is always created when the signal is received by agent j , and
3. an indirect effect on information transmission as messages m = 1 are more likely to be blocked by unbiased agents, since the message is less likely to be credible.
For unbiased agents who receive the same message as the unbiased agent whose status has switched, all effects concur to reduce expected utility. For biased agents, there is a trade-off. Both direct effects result in an increase in expected utility, but the indirect effect may induce a decrease in the number of unbiased agents who
Kranton I 435
receive and believe message m = 1.
The negative effect of adding biased agents stands in sharp contrast to models of rumors and opinion formation based on fixed laws of diffusion or adoption. In such models, it is always beneficial for biased agents to increase their numbers. Here, where agents strategically transmit messages from others, the introduction of more biased agents can reduce their expected utility, depending on where the agents are located in the network.
Kranton I 436
General Networks/Communication/Bloch/Demange/Kranton: We identify three key simplifying assumptions that render the analysis of the general network similar to the analysis of a tree.
1. If agents transmit a message, they send the message to all their neighbors (except the one from whom they have received a message). Communication is multicast, and agents cannot endogenously choose which route to send the message along.
2. The time it takes a message to travel along a path is proportional to the length of the path. This assumption is needed to guarantee that agents can identify the agents from whom they receive the message the first time as those agents who are at a shortest distance in the network. Absent this assumption, agents would have to make complex computations to identify the set of agents from whom they receive the message the first time.
3. [Most importantly] agents only decide whether or not to transmit the message the first time they receive it; that is, although a message could reach an agent along several paths and an agent could therefore receive several messages, they ignore all messages but the first one.
Kranton I 437
However, we observe that, even under the three assumptions on agents’ behavior, MCEs might not be defined when the network contains cycles.

Francis Bloch, Gabrielle Demange & Rachel Kranton, 2018. "Rumors And Social Networks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(2), pages 421-448.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kranton I
Rachel E. Kranton
Francis Bloch
Gabrielle Demange,
Rumors And Social Networks 2018

Kranton II
Rachel E. Kranton
George A. Akerlof
Identity Economics: How Our Identities Shape Our Work, Wages, and Well-Being Princeton 2011

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