Name: Alex Tevonyan Date: 3/7/2023 Section: 1D TA: Carmella Stoddard Group members: Talia Myers, Shana Adelpour 1) Flintheart Scrooge Stick with the plan Doublecross Stick with the plan (4,4) (0,8) Doublecross (8,0) (2,2) 2) The pure strategy Nash equilibria is a pair of strategies when a pair of strategies has multiple best responses due to the prioritization of one outcome over another due to a lack of opportunity to increase one’s outcome by changing one’s response. There is 1 Nash equilibrium in the network. The decisions could occur like this. If Flintheart chooses to stick to the plan, Flintheart will be able to acquire a maximum of four diamonds. Additionally, the same occurs for Scrooge if he sticks to the plan, as he can receive a maximum of four diamonds. Doublecrossing will be the best response if the other player sticks with the plan, as one can maximize the number of diamonds to 8 for both Scrooge and Flintheart. If Scrooge double crosses Flintheart, Scrooge will acquire 8 diamonds, and Flintheart will acquire 0 diamonds, and vice versa, as Flintheart, upon doublecrossing, will acquire 8 diamonds while Scrooge will not get any. Since both individuals have now decided to double-cross due to the desire to maximize their diamond acquisitions, the pay off for both will be 2 diamonds. The pure strategy Nash equilibrium will have a payoff of (2,2) due to the double-crossing strategy because in this strategic pair of decisions, a pure strategic Nash equilibrium occurs while describing a stable state in a game where each player can choose a single strategy, and no player can enhance their payoff by unilaterally changing their strategy. 3) The socially optimal outcomes must include the sum of each coordinate in the payoff Matrix so that the group's outcome maximizes the number of diamonds. Therefore, three outcomes are socially optimal: Flintheart sticks with the plan, and so does Scrooge; Flintheart sticks with the plan, but Scrooge doublecrosses; and Scrooge sticks with the plan while Flintheart doublecrosses. These outcomes are not realized because each duck would like to maximize their diamonds for all parties. In this case, we would not expect a socially optimal strategy to occur due to their emphasis on individual outcomes rather than group outcomes, deemphasizing individual outcomes. Flintheart Stick with the plan Flintheart Double Cross Scrooge Stick with the plan 4+4=8 4+4=8 Scrooge Double Cross 4+4=8 2+2=4 4) Ellie Joel early late early (40,40) (0,30) late (30,0) (20,20) 5) Going early for both Joel and Ellie is one of the Nash equilibria as both Joel and Ellie will lead to a payoff of 40 sheep each as getting 40 sheep is superior to getting 30 sheep. If Joel goes early, the best response for Ellie would be to go early because 40 is greater than 0. If Joel goes late, the best response for Ellie is to go late as that would maximize her payoff of 20 sheep, which is overall greater than 0. The two individuals have two types of nash equilibrium, in which both go early or late; this means neither player benefits from unilaterally changing their strategy. Ellie Joel early late early (40,40)=40+40=80 (0,30)=30+0=30 late (30,0)=30+0=30 (20,20)=20+20=40 6) The socially optimal strategy from the lens of risk dominance is minimizing one’s propensity to have a payoff of zero sheep. The socially optimal outcome, however, is both individuals going early as that will maximize the player's payoffs of 80 sheep. As a result of this, the strategy one must pursue is the one that allows one to avoid losing all of their sheep. As a result, the safest strategy is to choose late for both individuals. To avoid the outcome of receiving no sheep, therefore, both Ellie and Joel will choose to go late. This makes the socially optimal outcome unlikely to occur because individuals in this scenario do not want to be susceptible to being penalized by the other player’s actions. Joel, therefore, chooses to go late to prioritize risk dominance over payoff dominance. Joel may believe a payoff of 20 is superior to no payoff in case Ellie goes early, and in the opposite case, Ellie may also believe a payoff of 20 is superior to no payoff if Joel goes early. 7) a) yes, the outcome is stable. b) Each edge has a value of at least 1 when the value of both nodes connected to it is added up, making the outcome stable, meaning that it has no instabilities, which would result in a value that is less than 1. Additionally, since the outside edges have no way of leveraging any outside connections, there is a stable outcome leaving them with no way to disrupt the current network’s outcome and situation. For example, if one adds the values of the nodes C, B, and E, one can see that the nodes not in exchange with one another, such as B and E being added, ⅔+¾=17/12, E and C are added, ⅔+¾=17/12, B and C being added, ⅔+⅔=4/3. Since all of these edges’ sums are greater than 1, one can see that the network’s inner parts are stable. 8) a) no, the outcome is not balanced. b) i) SurplusE-F=1- (outside option E+ outside option F)= 1-(1-⅔+0)=⅔ SurplusE-F/2= ⅔/2 SurplusE/2 + outside option of E = ⅓+⅓=⅔ , ⅔ isn’t equal to ¾ it is unbalanced. SurplusF/2 + outside option of F=0+⅓ = ⅓ isn’t equal to ¼ therefore, it is unbalanced. ii)Surplus B-A=1-(outside option A+outside option B)=1-(0+(1-2/3)))= ⅔ /2=⅓ SurplusB/2 +outside option of B= ⅓+⅓= ⅔ , is equal to B’s value, of ⅔, meaning it is balanced. SurplusA/2 + outside option of A=⅓+0 =⅓ equals A’s value meaning it is balanced. iii) One can see if the Nash Bargaining solution’s trade equals each value exchange in the network; if any are unequal, it is unbalanced. 9) a) Nodes E and B are expected to make the most money. b) The nodes with the most money is due to the greatest number of outside options that don't have any outside options. They have the greatest bargaining power. As a result, B and E can leverage their outside connections to have the most bargaining power due to the highest number of neighbors. c) As shown above, the advantages which the most powerful nodes in a graph experience is most similar to the nodes on a 4 node path. As B can choose which nodes to include in the exchange of value and which to exclude and as a result must seek other nodes with outside options to exchange value with. 10) a) The study by the sociologists at Southern Trojan University will be better evidence of “universal” human social behavior. b)STU studied human social behavior across samples within different contexts and included more national diversity at BSU. There may be greater numbers, but it does not necessarily focus on multiple contexts concerning various diverse societies. Q1. Tommy’s search engine will, over time, lose power and give his competitors the upper hand via total transparency and allowing them to create an improved search engine that is superior to his current search engine, giving his company a disadvantage. Q2. a) The first company’s approach won’t work because no direct link is established to Josephine’s website; the indirect links will not increase the rank because this will not point to other nodes. PageRank involves the usefulness of information; if more pages point to one’s page, the PageRank increases, regardless of the other website’s rank making it insignificant as the other pages do not link to her. However, other restaurants and delivery companies could offer other benefits such as free delivery, creating competition and hurting her rankings in the process and other bigger websites are unlikely to link to her. b) As mentioned in the extra lecture, a high authority score is associated with several hubs pointing to a person’s website. The second company’s approach works better because the websites with higher-quality hub links are linked to Josephina’s website, increasing the authority score due to the websites that recommend Josephina’s. This will boost one’s affiliation via pages that link to good restaurants, increasing their Hub scores, and linking them to Josephina’s blog.
