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1. The Centrality of Black Identity for Black Students in Engineering

   Mobley, Catherine ; Brawner, Catherine E. ; Brent, Rebecca ; Orr, Marisa K. ( January 2021 , Collaborative Network for Engineering and Computing Diversity (CoNECD) Conference)

   Introduction and Theoretical Frameworks Our study draws upon several theoretical foundations to investigate and explain the educational experiences of Black students majoring in ME, CpE, and EE: intersectionality, critical race theory, and community cultural wealth theory. Intersectionality explains how gender operates together with race, not independently, to produce multiple, overlapping forms of discrimination and social inequality (Crenshaw, 1989; Collins, 2013). Critical race theory recognizes the unique experiences of marginalized groups and strives to identify the micro- and macro-institutional sources of discrimination and prejudice (Delgado & Stefancic, 2001). Community cultural wealth integrates an asset-based perspective to our analysis of engineering education to assist in the identification of factors that contribute to the success of engineering students (Yosso, 2005). These three theoretical frameworks are buttressed by our use of Racial Identity Theory, which expands understanding about the significance and meaning associated with students’ sense of group membership. Sellers and colleagues (1997) introduced the Multidimensional Model of Racial Identity (MMRI), in which they indicated that racial identity refers to the “significance and meaning that African Americans place on race in defining themselves” (p. 19). The development of this model was based on the reality that individuals vary greatly in the extent to which they attach meaning to being a member of the Black racial group. Sellers et al. (1997) posited that there are four components of racial identity: 1. Racial salience: “the extent to which one’s race is a relevant part of one’s self-concept at a particular moment or in a particular situation” (p. 24). 2. Racial centrality: “the extent to which a person normatively defines himself or herself with regard to race” (p. 25). 3. Racial regard: “a person’s affective or evaluative judgment of his or her race in terms of positive-negative valence” (p. 26). This element consists of public regard and private regard. 4. Racial ideology: “composed of the individual’s beliefs, opinions and attitudes with respect to the way he or she feels that the members of the race should act” (p. 27). The resulting 56-item inventory, the Multidimensional Inventory of Black Identity (MIBI), provides a robust measure of Black identity that can be used across multiple contexts. Research Questions Our 3-year, mixed-method study of Black students in computer (CpE), electrical (EE) and mechanical engineering (ME) aims to identify institutional policies and practices that contribute to the retention and attrition of Black students in electrical, computer, and mechanical engineering. Our four study institutions include historically Black institutions as well as predominantly white institutions, all of which are in the top 15 nationally in the number of Black engineering graduates. We are using a transformative mixed-methods design to answer the following overarching research questions: 1. Why do Black men and women choose and persist in, or leave, EE, CpE, and ME? 2. What are the academic trajectories of Black men and women in EE, CpE, and ME? 3. In what way do these pathways vary by gender or institution? 4. What institutional policies and practices promote greater retention of Black engineering students? Methods This study of Black students in CpE, EE, and ME reports initial results from in-depth interviews at one HBCU and one PWI. We asked students about a variety of topics, including their sense of belonging on campus and in the major, experiences with discrimination, the impact of race on their experiences, and experiences with microaggressions. For this paper, we draw on two methodological approaches that allowed us to move beyond a traditional, linear approach to in-depth interviews, allowing for more diverse experiences and narratives to emerge. First, we used an identity circle to gain a better understanding of the relative importance to the participants of racial identity, as compared to other identities. The identity circle is a series of three concentric circles, surrounding an “inner core” representing one’s “core self.” Participants were asked to place various identities from a provided list that included demographic, family-related, and school-related identities on the identity circle to reflect the relative importance of the different identities to participants’ current engineering education experiences. Second, participants were asked to complete an 8-item survey which measured the “centrality” of racial identity as defined by Sellers et al. (1997). Following Enders’ (2018) reflection on the MMRI and Nigrescence Theory, we chose to use the measure of racial centrality as it is generally more stable across situations and best “describes the place race holds in the hierarchy of identities an individual possesses and answers the question ‘How important is race to me in my life?’” (p. 518). Participants completed the MIBI items at the end of the interview to allow us to learn more about the participants’ identification with their racial group, to avoid biasing their responses to the Identity Circle, and to avoid potentially creating a stereotype threat at the beginning of the interview. This paper focuses on the results of the MIBI survey and the identity circles to investigate whether these measures were correlated. Recognizing that Blackness (race) is not monolithic, we were interested in knowing the extent to which the participants considered their Black identity as central to their engineering education experiences. Combined with discussion about the identity circles, this approach allowed us to learn more about how other elements of identity may shape the participants’ educational experiences and outcomes and revealed possible differences in how participants may enact various points of their identity. Findings For this paper, we focus on the results for five HBCU students and 27 PWI students who completed the MIBI and identity circle. The overall MIBI average for HBCU students was 43 (out of a possible 56) and the overall MIBI scores ranged from 36-51; the overall MIBI average for the PWI students was 40; the overall MIBI scores for the PWI students ranged from 24-51. Twenty-one students placed race in the inner circle, indicating that race was central to their identity. Five placed race on the second, middle circle; three placed race on the third, outer circle. Three students did not place race on their identity circle. For our cross-case qualitative analysis, we will choose cases across the two institutions that represent low, medium and high MIBI scores and different ranges of centrality of race to identity, as expressed in the identity circles. Our final analysis will include descriptive quotes from these in-depth interviews to further elucidate the significance of race to the participants’ identities and engineering education experiences. The results will provide context for our larger study of a total of 60 Black students in engineering at our four study institutions. Theoretically, our study represents a new application of Racial Identity Theory and will provide a unique opportunity to apply the theories of intersectionality, critical race theory, and community cultural wealth theory. Methodologically, our findings provide insights into the utility of combining our two qualitative research tools, the MIBI centrality scale and the identity circle, to better understand the influence of race on the education experiences of Black students in engineering. 

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2. Opting Into Optimal Matchings

   https://doi.org/10.1137/1.9781611974782.155  

   Blum, Avrim ; Caragiannis, Ioannis ; Haghtalab, Nika ; Procaccia, Ariel D. ; Procaccia, Eviatar B. ; Vaish, Rohit ( January 2017 , SIAM: ACM-SIAM Symposium on Discrete Algorithms (SODA17))

   We revisit the problem of designing optimal, individually rational matching mechanisms (in a general sense, allowing for cycles in directed graphs), where each player — who is associated with a subset of vertices — matches as many of his own vertices when he opts into the matching mechanism as when he opts out. We offer a new perspective on this problem by considering an arbitrary graph, but assuming that vertices are associated with players at random. Our main result asserts that, under certain conditions, any fixed optimal matching is likely to be individually rational up to lower-order terms. We also show that a simple and practical mechanism is (fully) individually rational, and likely to be optimal up to lower-order terms. We discuss the implications of our results for market design in general, and kidney exchange in particular. 

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3. Bayesian Multiagent Inverse Reinforcement Learning for Policy Recommendation

   Martin, C. ; Sandholm, T. ( January 2021 , AAAI-21 Workshop on Reinforcement Learning in Games)

   null (Ed.)

   We study the following problem, which to our knowledge has been addressed only partially in the literature and not in full generality. An agent observes two players play a zero-sum game that is known to the players but not the agent. The agent observes the actions and state transitions of their game play, but not rewards. The players may play either op-timally (according to some Nash equilibrium) or according to any other solution concept, such as a quantal response equilibrium. Following these observations, the agent must recommend a policy for one player, say Player 1. The goal is to recommend a policy that is minimally exploitable un-der the true, but unknown, game. We take a Bayesian ap-proach. We establish a likelihood function based on obser-vations and the specified solution concept. We then propose an approach based on Markov chain Monte Carlo (MCMC), which allows us to approximately sample games from the agent’s posterior belief distribution. Once we have a batch of independent samples from the posterior, we use linear pro-gramming and backward induction to compute a policy for Player 1 that minimizes the sum of exploitabilities over these games. This approximates the policy that minimizes the ex-pected exploitability under the full distribution. Our approach is also capable of handling counterfactuals, where known modifications are applied to the unknown game. We show that our Bayesian MCMC-based technique outperforms two other techniques—one based on the equilibrium policy of the maximum-probability game and the other based on imitation of observed behavior—on all the tested stochastic game envi-ronments. 

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4. A Two-Player Resource-Sharing Game with Asymmetric Information

   https://doi.org/10.3390/g14050061  

   Wijewardena, Mevan ; Neely, Michael J. ( October 2023 , Games)

   Yllka Velaj and Ulrich Berger (Ed.)

   This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an ϵ-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.

    

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5. On the existence of Nash Equilibrium in games with resource-bounded players

   Halpern, Joseph Y ; Pass, Rafael ; Reichman, Daniel ( September 2019 , Proceedings of the 12th International Symposium on A Game Theory (SAGT)})

   We consider computational games, sequences of games G = (G1,G2,...) where, for all n, Gn has the same set of players. Computational games arise in electronic money systems such as Bitcoin, in cryptographic protocols, and in the study of generative adversarial networks in machine learning. Assuming that one-way functions exist, we prove that there is 2-player zero-sum computational game G such that, for all n, the size of the action space in Gn is polynomial in n and the utility function in Gn is computable in time polynomial in n, and yet there is no ε-Nash equilibrium if players are restricted to using strategies computable by polynomial-time Turing machines, where we use a notion of Nash equilibrium that is tailored to computational games. We also show that an ε-Nash equilibrium may not exist if players are constrained to perform at most T computational steps in each of the games in the sequence. On the other hand, we show that if players can use arbitrary Turing machines to compute their strategies, then every computational game has an ε-Nash equilibrium. These results may shed light on competitive settings where the availability of more running time or faster algorithms can lead to a “computational arms race”, precluding the existence of equilibrium. They also point to inherent limitations of concepts such as “best response” and Nash equilibrium in games with resource-bounded players. 

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